[{"data":1,"prerenderedAt":43539},["ShallowReactive",2],{"note:math\u002Fode\u002F3-2&4-1 HW":3},{"id":4,"title":5,"body":6,"description":43519,"extension":43532,"meta":43533,"navigation":43534,"path":43535,"seo":43536,"stem":43537,"__hash__":43538},"notes\u002Fsource\u002Fmath\u002Fode\u002F3-2&4-1 HW.md","3-2 4-1 作业",{"type":7,"value":8,"toc":43518},"minimark",[9,14,17,22,29,45,50,489,491,495,500,661,776,781,1633,1637,1642,1846,2008,3506,3508,3512,3515,3519,4374,4379,5262,6452,8351,9020,9022,9026,9726,9730,9947,10339,10774,12296,13895,15281,15283,15286,15712,15719,15745,15747,15751,16309,16314,17171,18200,18206,18729,19862,19864,19868,19874,20240,20388,21835,22660,23033,24507,26120,26469,26471,26812,26971,27530,27535,30034,30040,30042,30503,31382,31844,32419,33234,33708,33713,34084,34399,34401,34405,34747,35183,35188,36547,37860,38679,38681,38685,38691,38700,38777,41588,41590,41594,41652,41663,41668],[10,11,13],"h1",{"id":12},"习题-32-41","习题 3.2 & 4.1",[15,16],"hr",{},[18,19,21],"h3",{"id":20},"第一步剖析问题-executive-summary","第一步：剖析问题 (Executive Summary)",[23,24,25],"p",{},[26,27,28],"strong",{},"核心任务：",[30,31,32,39],"ol",{},[33,34,35,38],"li",{},[26,36,37],{},"理解理论："," 解释常微分方程解的“生命周期”（即能延伸多远——延拓定理）以及解对“起跑线”（初值）的敏感程度（连续性与可微性）。",[33,40,41,44],{},[26,42,43],{},"应用实战："," 利用定理5中的微分公式（公式3.17和3.18）解决两个具体的计算问题。",[23,46,47],{},[26,48,49],{},"关键难点与隐含假设：",[51,52,53,376],"ul",{},[33,54,55,58,59,268,269,344,345,375],{},[26,56,57],{},"难点："," 理解 ",[60,61,64,110],"span",{"className":62},[63],"katex",[60,65,68],{"className":66},[67],"katex-mathml",[69,70,72],"math",{"xmlns":71},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[73,74,75,105],"semantics",{},[76,77,78],"mrow",{},[79,80,81,91],"mfrac",{},[76,82,83,88],{},[84,85,87],"mi",{"mathvariant":86},"normal","∂",[84,89,90],{},"φ",[76,92,93,95],{},[84,94,87],{"mathvariant":86},[96,97,98,101],"msub",{},[84,99,100],{},"y",[102,103,104],"mn",{},"0",[106,107,109],"annotation",{"encoding":108},"application\u002Fx-tex","\\frac{\\partial \\varphi}{\\partial y_0}",[60,111,115],{"className":112,"ariaHidden":114},[113],"katex-html","true",[60,116,119,124],{"className":117},[118],"katex-base",[60,120],{"className":121,"style":123},[122],"katex-strut","height:1.4133em;vertical-align:-0.4811em;",[60,125,128,133,264],{"className":126},[127],"mord",[60,129],{"className":130},[131,132],"mopen","nulldelimiter",[60,134,136],{"className":135},[79],[60,137,141,255],{"className":138},[139,140],"vlist-t","vlist-t2",[60,142,145,252],{"className":143},[144],"vlist-r",[60,146,150,223,234],{"className":147,"style":149},[148],"vlist","height:0.9322em;",[60,151,153,158],{"style":152},"top:-2.655em;",[60,154],{"className":155,"style":157},[156],"pstrut","height:3em;",[60,159,165],{"className":160},[161,162,163,164],"katex-sizing","reset-size6","size3","mtight",[60,166,168,172],{"className":167},[127,164],[60,169,87],{"className":170,"style":171},[127,164],"margin-right:0.0556em;",[60,173,175,180],{"className":174},[127,164],[60,176,100],{"className":177,"style":179},[127,178,164],"mathnormal","margin-right:0.0359em;",[60,181,184],{"className":182},[183],"msupsub",[60,185,187,214],{"className":186},[139,140],[60,188,190,209],{"className":189},[144],[60,191,194],{"className":192,"style":193},[148],"height:0.3173em;",[60,195,197,201],{"style":196},"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;",[60,198],{"className":199,"style":200},[156],"height:2.5em;",[60,202,206],{"className":203},[161,204,205,164],"reset-size3","size1",[60,207,104],{"className":208},[127,164],[60,210,213],{"className":211},[212],"vlist-s","​",[60,215,217],{"className":216},[144],[60,218,221],{"className":219,"style":220},[148],"height:0.143em;",[60,222],{},[60,224,226,229],{"style":225},"top:-3.23em;",[60,227],{"className":228,"style":157},[156],[60,230],{"className":231,"style":233},[232],"frac-line","border-bottom-width:0.04em;",[60,235,237,240],{"style":236},"top:-3.4461em;",[60,238],{"className":239,"style":157},[156],[60,241,243],{"className":242},[161,162,163,164],[60,244,246,249],{"className":245},[127,164],[60,247,87],{"className":248,"style":171},[127,164],[60,250,90],{"className":251},[127,178,164],[60,253,213],{"className":254},[212],[60,256,258],{"className":257},[144],[60,259,262],{"className":260,"style":261},[148],"height:0.4811em;",[60,263],{},[60,265],{"className":266},[267,132],"mclose"," 这种符号的物理意义。它代表的是“当初值 ",[60,270,272,290],{"className":271},[63],[60,273,275],{"className":274},[67],[69,276,277],{"xmlns":71},[73,278,279,287],{},[76,280,281],{},[96,282,283,285],{},[84,284,100],{},[102,286,104],{},[106,288,289],{"encoding":108},"y_0",[60,291,293],{"className":292,"ariaHidden":114},[113],[60,294,296,300],{"className":295},[118],[60,297],{"className":298,"style":299},[122],"height:0.625em;vertical-align:-0.1944em;",[60,301,303,306],{"className":302},[127],[60,304,100],{"className":305,"style":179},[127,178],[60,307,309],{"className":308},[183],[60,310,312,335],{"className":311},[139,140],[60,313,315,332],{"className":314},[144],[60,316,319],{"className":317,"style":318},[148],"height:0.3011em;",[60,320,322,326],{"style":321},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[60,323],{"className":324,"style":325},[156],"height:2.7em;",[60,327,329],{"className":328},[161,162,163,164],[60,330,104],{"className":331},[127,164],[60,333,213],{"className":334},[212],[60,336,338],{"className":337},[144],[60,339,342],{"className":340,"style":341},[148],"height:0.15em;",[60,343],{}," 变化一点点时，整个函数曲线在 ",[60,346,348,362],{"className":347},[63],[60,349,351],{"className":350},[67],[69,352,353],{"xmlns":71},[73,354,355,360],{},[76,356,357],{},[84,358,359],{},"x",[106,361,359],{"encoding":108},[60,363,365],{"className":364,"ariaHidden":114},[113],[60,366,368,372],{"className":367},[118],[60,369],{"className":370,"style":371},[122],"height:0.4306em;",[60,373,359],{"className":374},[127,178]," 处的变化率”。",[33,377,378,381,382,431,432,488],{},[26,379,380],{},"假设："," 在计算题目时，必须先知道“原方程的解 ",[60,383,385,409],{"className":384},[63],[60,386,388],{"className":387},[67],[69,389,390],{"xmlns":71},[73,391,392,406],{},[76,393,394,396,401,403],{},[84,395,90],{},[397,398,400],"mo",{"stretchy":399},"false","(",[84,402,359],{},[397,404,405],{"stretchy":399},")",[106,407,408],{"encoding":108},"\\varphi(x)",[60,410,412],{"className":411,"ariaHidden":114},[113],[60,413,415,419,422,425,428],{"className":414},[118],[60,416],{"className":417,"style":418},[122],"height:1em;vertical-align:-0.25em;",[60,420,90],{"className":421},[127,178],[60,423,400],{"className":424},[131],[60,426,359],{"className":427},[127,178],[60,429,405],{"className":430},[267]," 是什么”，才能将其代入积分公式中进行计算。特别是第2题，隐含了一个特解 ",[60,433,435,454],{"className":434},[63],[60,436,438],{"className":437},[67],[69,439,440],{"xmlns":71},[73,441,442,451],{},[76,443,444,446,449],{},[84,445,100],{},[397,447,448],{},"=",[102,450,104],{},[106,452,453],{"encoding":108},"y=0",[60,455,457,478],{"className":456,"ariaHidden":114},[113],[60,458,460,463,466,471,475],{"className":459},[118],[60,461],{"className":462,"style":299},[122],[60,464,100],{"className":465,"style":179},[127,178],[60,467],{"className":468,"style":470},[469],"mspace","margin-right:0.2778em;",[60,472,448],{"className":473},[474],"mrel",[60,476],{"className":477,"style":470},[469],[60,479,481,485],{"className":480},[118],[60,482],{"className":483,"style":484},[122],"height:0.6444em;",[60,486,104],{"className":487},[127],"。",[15,490],{},[18,492,494],{"id":493},"第二步深入分析理论-deep-dive","第二步：深入分析理论 (Deep Dive)",[496,497,499],"h4",{"id":498},"_1-解的延拓定理-extension-theorem-解的生命力","1. 解的延拓定理 (Extension Theorem) —— 解的“生命力”",[23,501,502,505,506,536,537,660],{},[26,503,504],{},"直观理解：","\n想象你在一个大广场（区域 ",[60,507,509,523],{"className":508},[63],[60,510,512],{"className":511},[67],[69,513,514],{"xmlns":71},[73,515,516,521],{},[76,517,518],{},[84,519,520],{},"G",[106,522,520],{"encoding":108},[60,524,526],{"className":525,"ariaHidden":114},[113],[60,527,529,533],{"className":528},[118],[60,530],{"className":531,"style":532},[122],"height:0.6833em;",[60,534,520],{"className":535},[127,178],"）上按照一张藏宝图（方程 ",[60,538,540,577],{"className":539},[63],[60,541,543],{"className":542},[67],[69,544,545],{"xmlns":71},[73,546,547,574],{},[76,548,549,558,560,563,565,567,570,572],{},[550,551,552,554],"msup",{},[84,553,100],{},[397,555,557],{"mathvariant":86,"lspace":556,"rspace":556},"0em","′",[397,559,448],{},[84,561,562],{},"f",[397,564,400],{"stretchy":399},[84,566,359],{},[397,568,569],{"separator":114},",",[84,571,100],{},[397,573,405],{"stretchy":399},[106,575,576],{"encoding":108},"y'=f(x,y)",[60,578,580,630],{"className":579,"ariaHidden":114},[113],[60,581,583,587,621,624,627],{"className":582},[118],[60,584],{"className":585,"style":586},[122],"height:0.9463em;vertical-align:-0.1944em;",[60,588,590,593],{"className":589},[127],[60,591,100],{"className":592,"style":179},[127,178],[60,594,596],{"className":595},[183],[60,597,599],{"className":598},[139],[60,600,602],{"className":601},[144],[60,603,606],{"className":604,"style":605},[148],"height:0.7519em;",[60,607,609,612],{"style":608},"top:-3.063em;margin-right:0.05em;",[60,610],{"className":611,"style":325},[156],[60,613,615],{"className":614},[161,162,163,164],[60,616,618],{"className":617},[127,164],[60,619,557],{"className":620},[127,164],[60,622],{"className":623,"style":470},[469],[60,625,448],{"className":626},[474],[60,628],{"className":629,"style":470},[469],[60,631,633,636,640,643,646,650,654,657],{"className":632},[118],[60,634],{"className":635,"style":418},[122],[60,637,562],{"className":638,"style":639},[127,178],"margin-right:0.1076em;",[60,641,400],{"className":642},[131],[60,644,359],{"className":645},[127,178],[60,647,569],{"className":648},[649],"mpunct",[60,651],{"className":652,"style":653},[469],"margin-right:0.1667em;",[60,655,100],{"className":656,"style":179},[127,178],[60,658,405],{"className":659},[267]," 指示的方向）行走。",[51,662,663,699],{},[33,664,665,668,669,698],{},[26,666,667],{},"定理的核心含义："," 只要你还在广场内，且指示方向是清晰的（",[60,670,672,685],{"className":671},[63],[60,673,675],{"className":674},[67],[69,676,677],{"xmlns":71},[73,678,679,683],{},[76,680,681],{},[84,682,562],{},[106,684,562],{"encoding":108},[60,686,688],{"className":687,"ariaHidden":114},[113],[60,689,691,695],{"className":690},[118],[60,692],{"className":693,"style":694},[122],"height:0.8889em;vertical-align:-0.1944em;",[60,696,562],{"className":697,"style":639},[127,178]," 连续且满足利普希茨条件），你就不会突然“卡住”或“消失”。你一定能一直走下去。",[33,700,701,704],{},[26,702,703],{},"停下来的原因只有两个：",[30,705,706,712],{},[33,707,708,711],{},[26,709,710],{},"撞墙了："," 你走到了广场的边缘（趋于边界）。",[33,713,714,717,718,746,747,775],{},[26,715,716],{},"飞出去了："," 你的速度变得无穷大，或者你走到了无穷远的地方（",[60,719,721,734],{"className":720},[63],[60,722,724],{"className":723},[67],[69,725,726],{"xmlns":71},[73,727,728,732],{},[76,729,730],{},[84,731,100],{},[106,733,100],{"encoding":108},[60,735,737],{"className":736,"ariaHidden":114},[113],[60,738,740,743],{"className":739},[118],[60,741],{"className":742,"style":299},[122],[60,744,100],{"className":745,"style":179},[127,178]," 无界或 ",[60,748,750,763],{"className":749},[63],[60,751,753],{"className":752},[67],[69,754,755],{"xmlns":71},[73,756,757,761],{},[76,758,759],{},[84,760,359],{},[106,762,359],{"encoding":108},[60,764,766],{"className":765,"ariaHidden":114},[113],[60,767,769,772],{"className":768},[118],[60,770],{"className":771,"style":371},[122],[60,773,359],{"className":774},[127,178]," 无界）。",[23,777,778],{},[26,779,780],{},"例1的深度解读：",[51,782,783,948,1237],{},[33,784,785,786,488],{},"方程 ",[60,787,789,831],{"className":788},[63],[60,790,792],{"className":791},[67],[69,793,794],{"xmlns":71},[73,795,796,828],{},[76,797,798,804,806,808,815,818,821,823,826],{},[550,799,800,802],{},[84,801,100],{},[397,803,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,805,448],{},[397,807,400],{"stretchy":399},[550,809,810,812],{},[84,811,100],{},[102,813,814],{},"2",[397,816,817],{},"−",[102,819,820],{},"1",[397,822,405],{"stretchy":399},[84,824,825],{"mathvariant":86},"\u002F",[102,827,814],{},[106,829,830],{"encoding":108},"y' = (y^2-1)\u002F2",[60,832,834,881,932],{"className":833,"ariaHidden":114},[113],[60,835,837,840,872,875,878],{"className":836},[118],[60,838],{"className":839,"style":586},[122],[60,841,843,846],{"className":842},[127],[60,844,100],{"className":845,"style":179},[127,178],[60,847,849],{"className":848},[183],[60,850,852],{"className":851},[139],[60,853,855],{"className":854},[144],[60,856,858],{"className":857,"style":605},[148],[60,859,860,863],{"style":608},[60,861],{"className":862,"style":325},[156],[60,864,866],{"className":865},[161,162,163,164],[60,867,869],{"className":868},[127,164],[60,870,557],{"className":871},[127,164],[60,873],{"className":874,"style":470},[469],[60,876,448],{"className":877},[474],[60,879],{"className":880,"style":470},[469],[60,882,884,888,891,921,925,929],{"className":883},[118],[60,885],{"className":886,"style":887},[122],"height:1.0641em;vertical-align:-0.25em;",[60,889,400],{"className":890},[131],[60,892,894,897],{"className":893},[127],[60,895,100],{"className":896,"style":179},[127,178],[60,898,900],{"className":899},[183],[60,901,903],{"className":902},[139],[60,904,906],{"className":905},[144],[60,907,910],{"className":908,"style":909},[148],"height:0.8141em;",[60,911,912,915],{"style":608},[60,913],{"className":914,"style":325},[156],[60,916,918],{"className":917},[161,162,163,164],[60,919,814],{"className":920},[127,164],[60,922],{"className":923,"style":924},[469],"margin-right:0.2222em;",[60,926,817],{"className":927},[928],"mbin",[60,930],{"className":931,"style":924},[469],[60,933,935,938,941,944],{"className":934},[118],[60,936],{"className":937,"style":418},[122],[60,939,820],{"className":940},[127],[60,942,405],{"className":943},[267],[60,945,947],{"className":946},[127],"\u002F2",[33,949,950,1168,1169,1204,1205,1233,1234,488],{},[26,951,952,953,1167],{},"解 ",[60,954,956,1000],{"className":955},[63],[60,957,959],{"className":958},[67],[69,960,961],{"xmlns":71},[73,962,963,997],{},[76,964,965,967,969],{},[84,966,100],{},[397,968,448],{},[79,970,971,984],{},[76,972,973,975,977],{},[102,974,820],{},[397,976,817],{},[550,978,979,982],{},[84,980,981],{},"e",[84,983,359],{},[76,985,986,988,991],{},[102,987,820],{},[397,989,990],{},"+",[550,992,993,995],{},[84,994,981],{},[84,996,359],{},[106,998,999],{"encoding":108},"y = \\frac{1-e^x}{1+e^x}",[60,1001,1003,1021],{"className":1002,"ariaHidden":114},[113],[60,1004,1006,1009,1012,1015,1018],{"className":1005},[118],[60,1007],{"className":1008,"style":299},[122],[60,1010,100],{"className":1011,"style":179},[127,178],[60,1013],{"className":1014,"style":470},[469],[60,1016,448],{"className":1017},[474],[60,1019],{"className":1020,"style":470},[469],[60,1022,1024,1028],{"className":1023},[118],[60,1025],{"className":1026,"style":1027},[122],"height:1.3143em;vertical-align:-0.4033em;",[60,1029,1031,1034,1164],{"className":1030},[127],[60,1032],{"className":1033},[131,132],[60,1035,1037],{"className":1036},[79],[60,1038,1040,1155],{"className":1039},[139,140],[60,1041,1043,1152],{"className":1042},[144],[60,1044,1047,1095,1103],{"className":1045,"style":1046},[148],"height:0.911em;",[60,1048,1049,1052],{"style":152},[60,1050],{"className":1051,"style":157},[156],[60,1053,1055],{"className":1054},[161,162,163,164],[60,1056,1058,1061,1064],{"className":1057},[127,164],[60,1059,820],{"className":1060},[127,164],[60,1062,990],{"className":1063},[928,164],[60,1065,1067,1070],{"className":1066},[127,164],[60,1068,981],{"className":1069},[127,178,164],[60,1071,1073],{"className":1072},[183],[60,1074,1076],{"className":1075},[139],[60,1077,1079],{"className":1078},[144],[60,1080,1083],{"className":1081,"style":1082},[148],"height:0.5935em;",[60,1084,1086,1089],{"style":1085},"top:-2.786em;margin-right:0.0714em;",[60,1087],{"className":1088,"style":200},[156],[60,1090,1092],{"className":1091},[161,204,205,164],[60,1093,359],{"className":1094},[127,178,164],[60,1096,1097,1100],{"style":225},[60,1098],{"className":1099,"style":157},[156],[60,1101],{"className":1102,"style":233},[232],[60,1104,1106,1109],{"style":1105},"top:-3.394em;",[60,1107],{"className":1108,"style":157},[156],[60,1110,1112],{"className":1111},[161,162,163,164],[60,1113,1115,1118,1121],{"className":1114},[127,164],[60,1116,820],{"className":1117},[127,164],[60,1119,817],{"className":1120},[928,164],[60,1122,1124,1127],{"className":1123},[127,164],[60,1125,981],{"className":1126},[127,178,164],[60,1128,1130],{"className":1129},[183],[60,1131,1133],{"className":1132},[139],[60,1134,1136],{"className":1135},[144],[60,1137,1140],{"className":1138,"style":1139},[148],"height:0.7385em;",[60,1141,1143,1146],{"style":1142},"top:-2.931em;margin-right:0.0714em;",[60,1144],{"className":1145,"style":200},[156],[60,1147,1149],{"className":1148},[161,204,205,164],[60,1150,359],{"className":1151},[127,178,164],[60,1153,213],{"className":1154},[212],[60,1156,1158],{"className":1157},[144],[60,1159,1162],{"className":1160,"style":1161},[148],"height:0.4033em;",[60,1163],{},[60,1165],{"className":1166},[267,132]," (过原点)："," 这个解被限制在 ",[60,1170,1172,1188],{"className":1171},[63],[60,1173,1175],{"className":1174},[67],[69,1176,1177],{"xmlns":71},[73,1178,1179,1185],{},[76,1180,1181,1183],{},[397,1182,817],{},[102,1184,820],{},[106,1186,1187],{"encoding":108},"-1",[60,1189,1191],{"className":1190,"ariaHidden":114},[113],[60,1192,1194,1198,1201],{"className":1193},[118],[60,1195],{"className":1196,"style":1197},[122],"height:0.7278em;vertical-align:-0.0833em;",[60,1199,817],{"className":1200},[127],[60,1202,820],{"className":1203},[127]," 到 ",[60,1206,1208,1221],{"className":1207},[63],[60,1209,1211],{"className":1210},[67],[69,1212,1213],{"xmlns":71},[73,1214,1215,1219],{},[76,1216,1217],{},[102,1218,820],{},[106,1220,820],{"encoding":108},[60,1222,1224],{"className":1223,"ariaHidden":114},[113],[60,1225,1227,1230],{"className":1226},[118],[60,1228],{"className":1229,"style":484},[122],[60,1231,820],{"className":1232},[127]," 之间，它永远不会变成无穷大，所以它可以一直向左右延伸到无穷远。这就是推论中的",[26,1235,1236],{},"情况1",[33,1238,1239,1518,1519,1571,1572,1600,1601,1604,1605,775],{},[26,1240,952,1241,1445,1446,1517],{},[60,1242,1244,1286],{"className":1243},[63],[60,1245,1247],{"className":1246},[67],[69,1248,1249],{"xmlns":71},[73,1250,1251,1283],{},[76,1252,1253,1255,1257],{},[84,1254,100],{},[397,1256,448],{},[79,1258,1259,1271],{},[76,1260,1261,1263,1265],{},[102,1262,820],{},[397,1264,990],{},[550,1266,1267,1269],{},[84,1268,981],{},[84,1270,359],{},[76,1272,1273,1275,1277],{},[102,1274,820],{},[397,1276,817],{},[550,1278,1279,1281],{},[84,1280,981],{},[84,1282,359],{},[106,1284,1285],{"encoding":108},"y = \\frac{1+e^x}{1-e^x}",[60,1287,1289,1307],{"className":1288,"ariaHidden":114},[113],[60,1290,1292,1295,1298,1301,1304],{"className":1291},[118],[60,1293],{"className":1294,"style":299},[122],[60,1296,100],{"className":1297,"style":179},[127,178],[60,1299],{"className":1300,"style":470},[469],[60,1302,448],{"className":1303},[474],[60,1305],{"className":1306,"style":470},[469],[60,1308,1310,1313],{"className":1309},[118],[60,1311],{"className":1312,"style":1027},[122],[60,1314,1316,1319,1442],{"className":1315},[127],[60,1317],{"className":1318},[131,132],[60,1320,1322],{"className":1321},[79],[60,1323,1325,1434],{"className":1324},[139,140],[60,1326,1328,1431],{"className":1327},[144],[60,1329,1331,1377,1385],{"className":1330,"style":1046},[148],[60,1332,1333,1336],{"style":152},[60,1334],{"className":1335,"style":157},[156],[60,1337,1339],{"className":1338},[161,162,163,164],[60,1340,1342,1345,1348],{"className":1341},[127,164],[60,1343,820],{"className":1344},[127,164],[60,1346,817],{"className":1347},[928,164],[60,1349,1351,1354],{"className":1350},[127,164],[60,1352,981],{"className":1353},[127,178,164],[60,1355,1357],{"className":1356},[183],[60,1358,1360],{"className":1359},[139],[60,1361,1363],{"className":1362},[144],[60,1364,1366],{"className":1365,"style":1082},[148],[60,1367,1368,1371],{"style":1085},[60,1369],{"className":1370,"style":200},[156],[60,1372,1374],{"className":1373},[161,204,205,164],[60,1375,359],{"className":1376},[127,178,164],[60,1378,1379,1382],{"style":225},[60,1380],{"className":1381,"style":157},[156],[60,1383],{"className":1384,"style":233},[232],[60,1386,1387,1390],{"style":1105},[60,1388],{"className":1389,"style":157},[156],[60,1391,1393],{"className":1392},[161,162,163,164],[60,1394,1396,1399,1402],{"className":1395},[127,164],[60,1397,820],{"className":1398},[127,164],[60,1400,990],{"className":1401},[928,164],[60,1403,1405,1408],{"className":1404},[127,164],[60,1406,981],{"className":1407},[127,178,164],[60,1409,1411],{"className":1410},[183],[60,1412,1414],{"className":1413},[139],[60,1415,1417],{"className":1416},[144],[60,1418,1420],{"className":1419,"style":1139},[148],[60,1421,1422,1425],{"style":1142},[60,1423],{"className":1424,"style":200},[156],[60,1426,1428],{"className":1427},[161,204,205,164],[60,1429,359],{"className":1430},[127,178,164],[60,1432,213],{"className":1433},[212],[60,1435,1437],{"className":1436},[144],[60,1438,1440],{"className":1439,"style":1161},[148],[60,1441],{},[60,1443],{"className":1444},[267,132]," (过 ",[60,1447,1449,1480],{"className":1448},[63],[60,1450,1452],{"className":1451},[67],[69,1453,1454],{"xmlns":71},[73,1455,1456,1477],{},[76,1457,1458,1460,1463,1466,1468,1470,1472,1475],{},[397,1459,400],{"stretchy":399},[84,1461,1462],{},"ln",[397,1464,1465],{},"⁡",[102,1467,814],{},[397,1469,569],{"separator":114},[397,1471,817],{},[102,1473,1474],{},"3",[397,1476,405],{"stretchy":399},[106,1478,1479],{"encoding":108},"(\\ln 2, -3)",[60,1481,1483],{"className":1482,"ariaHidden":114},[113],[60,1484,1486,1489,1492,1496,1499,1502,1505,1508,1511,1514],{"className":1485},[118],[60,1487],{"className":1488,"style":418},[122],[60,1490,400],{"className":1491},[131],[60,1493,1462],{"className":1494},[1495],"mop",[60,1497],{"className":1498,"style":653},[469],[60,1500,814],{"className":1501},[127],[60,1503,569],{"className":1504},[649],[60,1506],{"className":1507,"style":653},[469],[60,1509,817],{"className":1510},[127],[60,1512,1474],{"className":1513},[127],[60,1515,405],{"className":1516},[267],")："," 当 ",[60,1520,1522,1541],{"className":1521},[63],[60,1523,1525],{"className":1524},[67],[69,1526,1527],{"xmlns":71},[73,1528,1529,1538],{},[76,1530,1531,1533,1536],{},[84,1532,359],{},[397,1534,1535],{},"→",[102,1537,104],{},[106,1539,1540],{"encoding":108},"x \\to 0",[60,1542,1544,1562],{"className":1543,"ariaHidden":114},[113],[60,1545,1547,1550,1553,1556,1559],{"className":1546},[118],[60,1548],{"className":1549,"style":371},[122],[60,1551,359],{"className":1552},[127,178],[60,1554],{"className":1555,"style":470},[469],[60,1557,1535],{"className":1558},[474],[60,1560],{"className":1561,"style":470},[469],[60,1563,1565,1568],{"className":1564},[118],[60,1566],{"className":1567,"style":484},[122],[60,1569,104],{"className":1570},[127]," 时，分母趋近于0，整个 ",[60,1573,1575,1588],{"className":1574},[63],[60,1576,1578],{"className":1577},[67],[69,1579,1580],{"xmlns":71},[73,1581,1582,1586],{},[76,1583,1584],{},[84,1585,100],{},[106,1587,100],{"encoding":108},[60,1589,1591],{"className":1590,"ariaHidden":114},[113],[60,1592,1594,1597],{"className":1593},[118],[60,1595],{"className":1596,"style":299},[122],[60,1598,100],{"className":1599,"style":179},[127,178]," 趋向于无穷大。这意味着解“爆炸”了。这就是推论中的",[26,1602,1603],{},"情况2","（",[60,1606,1608,1621],{"className":1607},[63],[60,1609,1611],{"className":1610},[67],[69,1612,1613],{"xmlns":71},[73,1614,1615,1619],{},[76,1616,1617],{},[84,1618,100],{},[106,1620,100],{"encoding":108},[60,1622,1624],{"className":1623,"ariaHidden":114},[113],[60,1625,1627,1630],{"className":1626},[118],[60,1628],{"className":1629,"style":299},[122],[60,1631,100],{"className":1632,"style":179},[127,178],[496,1634,1636],{"id":1635},"_2-解对初值的依赖-dependence-on-initial-values-失之毫厘谬以千里","2. 解对初值的依赖 (Dependence on Initial Values) —— “失之毫厘，谬以千里”",[23,1638,1639,1641],{},[26,1640,504],{},"\n想象射击。",[51,1643,1644,1650],{},[33,1645,1646,1649],{},[26,1647,1648],{},"连续性 (定理4)："," 你的手抖了一下（初值变动一点点），子弹的落点只会偏一点点，不会突然飞到背后去。",[33,1651,1652,1655,1656,1659,1660],{},[26,1653,1654],{},"可微性 (定理5)："," 我们不仅想知道偏了，还想知道",[26,1657,1658],{},"偏了多少","。\n",[51,1661,1662],{},[33,1663,1664,1816,1817,1845],{},[60,1665,1667,1696],{"className":1666},[63],[60,1668,1670],{"className":1669},[67],[69,1671,1672],{"xmlns":71},[73,1673,1674,1694],{},[76,1675,1676],{},[79,1677,1678,1684],{},[76,1679,1680,1682],{},[84,1681,87],{"mathvariant":86},[84,1683,90],{},[76,1685,1686,1688],{},[84,1687,87],{"mathvariant":86},[96,1689,1690,1692],{},[84,1691,100],{},[102,1693,104],{},[106,1695,109],{"encoding":108},[60,1697,1699],{"className":1698,"ariaHidden":114},[113],[60,1700,1702,1705],{"className":1701},[118],[60,1703],{"className":1704,"style":123},[122],[60,1706,1708,1711,1813],{"className":1707},[127],[60,1709],{"className":1710},[131,132],[60,1712,1714],{"className":1713},[79],[60,1715,1717,1805],{"className":1716},[139,140],[60,1718,1720,1802],{"className":1719},[144],[60,1721,1723,1777,1785],{"className":1722,"style":149},[148],[60,1724,1725,1728],{"style":152},[60,1726],{"className":1727,"style":157},[156],[60,1729,1731],{"className":1730},[161,162,163,164],[60,1732,1734,1737],{"className":1733},[127,164],[60,1735,87],{"className":1736,"style":171},[127,164],[60,1738,1740,1743],{"className":1739},[127,164],[60,1741,100],{"className":1742,"style":179},[127,178,164],[60,1744,1746],{"className":1745},[183],[60,1747,1749,1769],{"className":1748},[139,140],[60,1750,1752,1766],{"className":1751},[144],[60,1753,1755],{"className":1754,"style":193},[148],[60,1756,1757,1760],{"style":196},[60,1758],{"className":1759,"style":200},[156],[60,1761,1763],{"className":1762},[161,204,205,164],[60,1764,104],{"className":1765},[127,164],[60,1767,213],{"className":1768},[212],[60,1770,1772],{"className":1771},[144],[60,1773,1775],{"className":1774,"style":220},[148],[60,1776],{},[60,1778,1779,1782],{"style":225},[60,1780],{"className":1781,"style":157},[156],[60,1783],{"className":1784,"style":233},[232],[60,1786,1787,1790],{"style":236},[60,1788],{"className":1789,"style":157},[156],[60,1791,1793],{"className":1792},[161,162,163,164],[60,1794,1796,1799],{"className":1795},[127,164],[60,1797,87],{"className":1798,"style":171},[127,164],[60,1800,90],{"className":1801},[127,178,164],[60,1803,213],{"className":1804},[212],[60,1806,1808],{"className":1807},[144],[60,1809,1811],{"className":1810,"style":261},[148],[60,1812],{},[60,1814],{"className":1815},[267,132],"：不仅是连续的，还是光滑的，我们可以精确计算出“初值改变 1 单位，解在 ",[60,1818,1820,1833],{"className":1819},[63],[60,1821,1823],{"className":1822},[67],[69,1824,1825],{"xmlns":71},[73,1826,1827,1831],{},[76,1828,1829],{},[84,1830,359],{},[106,1832,359],{"encoding":108},[60,1834,1836],{"className":1835,"ariaHidden":114},[113],[60,1837,1839,1842],{"className":1838},[118],[60,1840],{"className":1841,"style":371},[122],[60,1843,359],{"className":1844},[127,178]," 处改变多少单位”。",[23,1847,1848,1851,1852,1881,1882,2007],{},[26,1849,1850],{},"公式解读（至关重要）：","\n我们要计算的是解 ",[60,1853,1855,1869],{"className":1854},[63],[60,1856,1858],{"className":1857},[67],[69,1859,1860],{"xmlns":71},[73,1861,1862,1866],{},[76,1863,1864],{},[84,1865,90],{},[106,1867,1868],{"encoding":108},"\\varphi",[60,1870,1872],{"className":1871,"ariaHidden":114},[113],[60,1873,1875,1878],{"className":1874},[118],[60,1876],{"className":1877,"style":299},[122],[60,1879,90],{"className":1880},[127,178]," 对初值 ",[60,1883,1885,1911],{"className":1884},[63],[60,1886,1888],{"className":1887},[67],[69,1889,1890],{"xmlns":71},[73,1891,1892,1908],{},[76,1893,1894,1900,1902],{},[96,1895,1896,1898],{},[84,1897,359],{},[102,1899,104],{},[397,1901,569],{"separator":114},[96,1903,1904,1906],{},[84,1905,100],{},[102,1907,104],{},[106,1909,1910],{"encoding":108},"x_0, y_0",[60,1912,1914],{"className":1913,"ariaHidden":114},[113],[60,1915,1917,1920,1961,1964,1967],{"className":1916},[118],[60,1918],{"className":1919,"style":299},[122],[60,1921,1923,1926],{"className":1922},[127],[60,1924,359],{"className":1925},[127,178],[60,1927,1929],{"className":1928},[183],[60,1930,1932,1953],{"className":1931},[139,140],[60,1933,1935,1950],{"className":1934},[144],[60,1936,1938],{"className":1937,"style":318},[148],[60,1939,1941,1944],{"style":1940},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[60,1942],{"className":1943,"style":325},[156],[60,1945,1947],{"className":1946},[161,162,163,164],[60,1948,104],{"className":1949},[127,164],[60,1951,213],{"className":1952},[212],[60,1954,1956],{"className":1955},[144],[60,1957,1959],{"className":1958,"style":341},[148],[60,1960],{},[60,1962,569],{"className":1963},[649],[60,1965],{"className":1966,"style":653},[469],[60,1968,1970,1973],{"className":1969},[127],[60,1971,100],{"className":1972,"style":179},[127,178],[60,1974,1976],{"className":1975},[183],[60,1977,1979,1999],{"className":1978},[139,140],[60,1980,1982,1996],{"className":1981},[144],[60,1983,1985],{"className":1984,"style":318},[148],[60,1986,1987,1990],{"style":321},[60,1988],{"className":1989,"style":325},[156],[60,1991,1993],{"className":1992},[161,162,163,164],[60,1994,104],{"className":1995},[127,164],[60,1997,213],{"className":1998},[212],[60,2000,2002],{"className":2001},[144],[60,2003,2005],{"className":2004,"style":341},[148],[60,2006],{}," 的偏导数。这里有两个现成的公式（无需死记硬背，但要会用）：",[51,2009,2010,2699],{},[33,2011,2012,2085,2549],{},[26,2013,2014,2015,2084],{},"公式 (3.18) 对 ",[60,2016,2018,2035],{"className":2017},[63],[60,2019,2021],{"className":2020},[67],[69,2022,2023],{"xmlns":71},[73,2024,2025,2033],{},[76,2026,2027],{},[96,2028,2029,2031],{},[84,2030,100],{},[102,2032,104],{},[106,2034,289],{"encoding":108},[60,2036,2038],{"className":2037,"ariaHidden":114},[113],[60,2039,2041,2044],{"className":2040},[118],[60,2042],{"className":2043,"style":299},[122],[60,2045,2047,2050],{"className":2046},[127],[60,2048,100],{"className":2049,"style":179},[127,178],[60,2051,2053],{"className":2052},[183],[60,2054,2056,2076],{"className":2055},[139,140],[60,2057,2059,2073],{"className":2058},[144],[60,2060,2062],{"className":2061,"style":318},[148],[60,2063,2064,2067],{"style":321},[60,2065],{"className":2066,"style":325},[156],[60,2068,2070],{"className":2069},[161,162,163,164],[60,2071,104],{"className":2072},[127,164],[60,2074,213],{"className":2075},[212],[60,2077,2079],{"className":2078},[144],[60,2080,2082],{"className":2081,"style":341},[148],[60,2083],{}," 的偏导：",[60,2086,2088,2181],{"className":2087},[63],[60,2089,2091],{"className":2090},[67],[69,2092,2093],{"xmlns":71},[73,2094,2095,2178],{},[76,2096,2097,2115,2117,2120,2122],{},[79,2098,2099,2105],{},[76,2100,2101,2103],{},[84,2102,87],{"mathvariant":86},[84,2104,90],{},[76,2106,2107,2109],{},[84,2108,87],{"mathvariant":86},[96,2110,2111,2113],{},[84,2112,100],{},[102,2114,104],{},[397,2116,448],{},[84,2118,2119],{},"exp",[397,2121,1465],{},[76,2123,2124,2126,2140,2171,2174,2176],{},[397,2125,400],{"fence":114},[2127,2128,2129,2132,2138],"msubsup",{},[397,2130,2131],{},"∫",[96,2133,2134,2136],{},[84,2135,359],{},[102,2137,104],{},[84,2139,359],{},[79,2141,2142,2165],{},[76,2143,2144,2146,2148,2150,2153,2155,2157,2159,2161,2163],{},[84,2145,87],{"mathvariant":86},[84,2147,562],{},[397,2149,400],{"stretchy":399},[84,2151,2152],{},"t",[397,2154,569],{"separator":114},[84,2156,90],{},[397,2158,400],{"stretchy":399},[84,2160,2152],{},[397,2162,405],{"stretchy":399},[397,2164,405],{"stretchy":399},[76,2166,2167,2169],{},[84,2168,87],{"mathvariant":86},[84,2170,100],{},[84,2172,2173],{},"d",[84,2175,2152],{},[397,2177,405],{"fence":114},[106,2179,2180],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial y_0} = \\exp\\left( \\int_{x_0}^x \\frac{\\partial f(t,\\varphi(t))}{\\partial y} dt \\right)",[60,2182,2184,2310],{"className":2183,"ariaHidden":114},[113],[60,2185,2187,2190,2301,2304,2307],{"className":2186},[118],[60,2188],{"className":2189,"style":123},[122],[60,2191,2193,2196,2298],{"className":2192},[127],[60,2194],{"className":2195},[131,132],[60,2197,2199],{"className":2198},[79],[60,2200,2202,2290],{"className":2201},[139,140],[60,2203,2205,2287],{"className":2204},[144],[60,2206,2208,2262,2270],{"className":2207,"style":149},[148],[60,2209,2210,2213],{"style":152},[60,2211],{"className":2212,"style":157},[156],[60,2214,2216],{"className":2215},[161,162,163,164],[60,2217,2219,2222],{"className":2218},[127,164],[60,2220,87],{"className":2221,"style":171},[127,164],[60,2223,2225,2228],{"className":2224},[127,164],[60,2226,100],{"className":2227,"style":179},[127,178,164],[60,2229,2231],{"className":2230},[183],[60,2232,2234,2254],{"className":2233},[139,140],[60,2235,2237,2251],{"className":2236},[144],[60,2238,2240],{"className":2239,"style":193},[148],[60,2241,2242,2245],{"style":196},[60,2243],{"className":2244,"style":200},[156],[60,2246,2248],{"className":2247},[161,204,205,164],[60,2249,104],{"className":2250},[127,164],[60,2252,213],{"className":2253},[212],[60,2255,2257],{"className":2256},[144],[60,2258,2260],{"className":2259,"style":220},[148],[60,2261],{},[60,2263,2264,2267],{"style":225},[60,2265],{"className":2266,"style":157},[156],[60,2268],{"className":2269,"style":233},[232],[60,2271,2272,2275],{"style":236},[60,2273],{"className":2274,"style":157},[156],[60,2276,2278],{"className":2277},[161,162,163,164],[60,2279,2281,2284],{"className":2280},[127,164],[60,2282,87],{"className":2283,"style":171},[127,164],[60,2285,90],{"className":2286},[127,178,164],[60,2288,213],{"className":2289},[212],[60,2291,2293],{"className":2292},[144],[60,2294,2296],{"className":2295,"style":261},[148],[60,2297],{},[60,2299],{"className":2300},[267,132],[60,2302],{"className":2303,"style":470},[469],[60,2305,448],{"className":2306},[474],[60,2308],{"className":2309,"style":470},[469],[60,2311,2313,2317,2320,2323],{"className":2312},[118],[60,2314],{"className":2315,"style":2316},[122],"height:1.8em;vertical-align:-0.65em;",[60,2318,2119],{"className":2319},[1495],[60,2321],{"className":2322,"style":653},[469],[60,2324,2327,2337,2436,2439,2537,2540,2543],{"className":2325},[2326],"minner",[60,2328,2332],{"className":2329,"style":2331},[131,2330],"delimcenter","top:0em;",[60,2333,400],{"className":2334},[2335,2336],"delimsizing","size2",[60,2338,2340,2346],{"className":2339},[1495],[60,2341,2131],{"className":2342,"style":2345},[1495,2343,2344],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[60,2347,2349],{"className":2348},[183],[60,2350,2352,2427],{"className":2351},[139,140],[60,2353,2355,2424],{"className":2354},[144],[60,2356,2359,2412],{"className":2357,"style":2358},[148],"height:0.8593em;",[60,2360,2362,2365],{"style":2361},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[60,2363],{"className":2364,"style":325},[156],[60,2366,2368],{"className":2367},[161,162,163,164],[60,2369,2371],{"className":2370},[127,164],[60,2372,2374,2377],{"className":2373},[127,164],[60,2375,359],{"className":2376},[127,178,164],[60,2378,2380],{"className":2379},[183],[60,2381,2383,2404],{"className":2382},[139,140],[60,2384,2386,2401],{"className":2385},[144],[60,2387,2389],{"className":2388,"style":193},[148],[60,2390,2392,2395],{"style":2391},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[60,2393],{"className":2394,"style":200},[156],[60,2396,2398],{"className":2397},[161,204,205,164],[60,2399,104],{"className":2400},[127,164],[60,2402,213],{"className":2403},[212],[60,2405,2407],{"className":2406},[144],[60,2408,2410],{"className":2409,"style":220},[148],[60,2411],{},[60,2413,2415,2418],{"style":2414},"top:-3.2579em;margin-right:0.05em;",[60,2416],{"className":2417,"style":325},[156],[60,2419,2421],{"className":2420},[161,162,163,164],[60,2422,359],{"className":2423},[127,178,164],[60,2425,213],{"className":2426},[212],[60,2428,2430],{"className":2429},[144],[60,2431,2434],{"className":2432,"style":2433},[148],"height:0.4559em;",[60,2435],{},[60,2437],{"className":2438,"style":653},[469],[60,2440,2442,2445,2534],{"className":2441},[127],[60,2443],{"className":2444},[131,132],[60,2446,2448],{"className":2447},[79],[60,2449,2451,2526],{"className":2450},[139,140],[60,2452,2454,2523],{"className":2453},[144],[60,2455,2458,2475,2483],{"className":2456,"style":2457},[148],"height:1.01em;",[60,2459,2460,2463],{"style":152},[60,2461],{"className":2462,"style":157},[156],[60,2464,2466],{"className":2465},[161,162,163,164],[60,2467,2469,2472],{"className":2468},[127,164],[60,2470,87],{"className":2471,"style":171},[127,164],[60,2473,100],{"className":2474,"style":179},[127,178,164],[60,2476,2477,2480],{"style":225},[60,2478],{"className":2479,"style":157},[156],[60,2481],{"className":2482,"style":233},[232],[60,2484,2486,2489],{"style":2485},"top:-3.485em;",[60,2487],{"className":2488,"style":157},[156],[60,2490,2492],{"className":2491},[161,162,163,164],[60,2493,2495,2498,2501,2504,2507,2510,2513,2516,2519],{"className":2494},[127,164],[60,2496,87],{"className":2497,"style":171},[127,164],[60,2499,562],{"className":2500,"style":639},[127,178,164],[60,2502,400],{"className":2503},[131,164],[60,2505,2152],{"className":2506},[127,178,164],[60,2508,569],{"className":2509},[649,164],[60,2511,90],{"className":2512},[127,178,164],[60,2514,400],{"className":2515},[131,164],[60,2517,2152],{"className":2518},[127,178,164],[60,2520,2522],{"className":2521},[267,164],"))",[60,2524,213],{"className":2525},[212],[60,2527,2529],{"className":2528},[144],[60,2530,2532],{"className":2531,"style":261},[148],[60,2533],{},[60,2535],{"className":2536},[267,132],[60,2538,2173],{"className":2539},[127,178],[60,2541,2152],{"className":2542},[127,178],[60,2544,2546],{"className":2545,"style":2331},[267,2330],[60,2547,405],{"className":2548},[2335,2336],[51,2550,2551],{},[33,2552,2553,2556,2557,2669,2670,2698],{},[26,2554,2555],{},"含义："," 这是一个指数累积的过程。",[60,2558,2560,2586],{"className":2559},[63],[60,2561,2563],{"className":2562},[67],[69,2564,2565],{"xmlns":71},[73,2566,2567,2583],{},[76,2568,2569],{},[79,2570,2571,2577],{},[76,2572,2573,2575],{},[84,2574,87],{"mathvariant":86},[84,2576,562],{},[76,2578,2579,2581],{},[84,2580,87],{"mathvariant":86},[84,2582,100],{},[106,2584,2585],{"encoding":108},"\\frac{\\partial f}{\\partial y}",[60,2587,2589],{"className":2588,"ariaHidden":114},[113],[60,2590,2592,2595],{"className":2591},[118],[60,2593],{"className":2594,"style":123},[122],[60,2596,2598,2601,2666],{"className":2597},[127],[60,2599],{"className":2600},[131,132],[60,2602,2604],{"className":2603},[79],[60,2605,2607,2658],{"className":2606},[139,140],[60,2608,2610,2655],{"className":2609},[144],[60,2611,2613,2630,2638],{"className":2612,"style":149},[148],[60,2614,2615,2618],{"style":152},[60,2616],{"className":2617,"style":157},[156],[60,2619,2621],{"className":2620},[161,162,163,164],[60,2622,2624,2627],{"className":2623},[127,164],[60,2625,87],{"className":2626,"style":171},[127,164],[60,2628,100],{"className":2629,"style":179},[127,178,164],[60,2631,2632,2635],{"style":225},[60,2633],{"className":2634,"style":157},[156],[60,2636],{"className":2637,"style":233},[232],[60,2639,2640,2643],{"style":236},[60,2641],{"className":2642,"style":157},[156],[60,2644,2646],{"className":2645},[161,162,163,164],[60,2647,2649,2652],{"className":2648},[127,164],[60,2650,87],{"className":2651,"style":171},[127,164],[60,2653,562],{"className":2654,"style":639},[127,178,164],[60,2656,213],{"className":2657},[212],[60,2659,2661],{"className":2660},[144],[60,2662,2664],{"className":2663,"style":261},[148],[60,2665],{},[60,2667],{"className":2668},[267,132]," 就像是一个“放大系数”，如果它大于0，初值的微小误差会随着 ",[60,2671,2673,2686],{"className":2672},[63],[60,2674,2676],{"className":2675},[67],[69,2677,2678],{"xmlns":71},[73,2679,2680,2684],{},[76,2681,2682],{},[84,2683,359],{},[106,2685,359],{"encoding":108},[60,2687,2689],{"className":2688,"ariaHidden":114},[113],[60,2690,2692,2695],{"className":2691},[118],[60,2693],{"className":2694,"style":371},[122],[60,2696,359],{"className":2697},[127,178]," 增大而指数级放大。",[33,2700,2701,2775,3214],{},[26,2702,2703,2704,2084],{},"公式 (3.17) 对 ",[60,2705,2707,2725],{"className":2706},[63],[60,2708,2710],{"className":2709},[67],[69,2711,2712],{"xmlns":71},[73,2713,2714,2722],{},[76,2715,2716],{},[96,2717,2718,2720],{},[84,2719,359],{},[102,2721,104],{},[106,2723,2724],{"encoding":108},"x_0",[60,2726,2728],{"className":2727,"ariaHidden":114},[113],[60,2729,2731,2735],{"className":2730},[118],[60,2732],{"className":2733,"style":2734},[122],"height:0.5806em;vertical-align:-0.15em;",[60,2736,2738,2741],{"className":2737},[127],[60,2739,359],{"className":2740},[127,178],[60,2742,2744],{"className":2743},[183],[60,2745,2747,2767],{"className":2746},[139,140],[60,2748,2750,2764],{"className":2749},[144],[60,2751,2753],{"className":2752,"style":318},[148],[60,2754,2755,2758],{"style":1940},[60,2756],{"className":2757,"style":325},[156],[60,2759,2761],{"className":2760},[161,162,163,164],[60,2762,104],{"className":2763},[127,164],[60,2765,213],{"className":2766},[212],[60,2768,2770],{"className":2769},[144],[60,2771,2773],{"className":2772,"style":341},[148],[60,2774],{},[60,2776,2778,2853],{"className":2777},[63],[60,2779,2781],{"className":2780},[67],[69,2782,2783],{"xmlns":71},[73,2784,2785,2850],{},[76,2786,2787,2805,2807,2809,2811,2813,2819,2821,2827,2829,2832],{},[79,2788,2789,2795],{},[76,2790,2791,2793],{},[84,2792,87],{"mathvariant":86},[84,2794,90],{},[76,2796,2797,2799],{},[84,2798,87],{"mathvariant":86},[96,2800,2801,2803],{},[84,2802,359],{},[102,2804,104],{},[397,2806,448],{},[397,2808,817],{},[84,2810,562],{},[397,2812,400],{"stretchy":399},[96,2814,2815,2817],{},[84,2816,359],{},[102,2818,104],{},[397,2820,569],{"separator":114},[96,2822,2823,2825],{},[84,2824,100],{},[102,2826,104],{},[397,2828,405],{"stretchy":399},[397,2830,2831],{},"⋅",[79,2833,2834,2840],{},[76,2835,2836,2838],{},[84,2837,87],{"mathvariant":86},[84,2839,90],{},[76,2841,2842,2844],{},[84,2843,87],{"mathvariant":86},[96,2845,2846,2848],{},[84,2847,100],{},[102,2849,104],{},[106,2851,2852],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial x_0} = -f(x_0,y_0) \\cdot \\frac{\\partial \\varphi}{\\partial y_0}",[60,2854,2856,2984,3097],{"className":2855,"ariaHidden":114},[113],[60,2857,2859,2863,2975,2978,2981],{"className":2858},[118],[60,2860],{"className":2861,"style":2862},[122],"height:1.3773em;vertical-align:-0.4451em;",[60,2864,2866,2869,2972],{"className":2865},[127],[60,2867],{"className":2868},[131,132],[60,2870,2872],{"className":2871},[79],[60,2873,2875,2963],{"className":2874},[139,140],[60,2876,2878,2960],{"className":2877},[144],[60,2879,2881,2935,2943],{"className":2880,"style":149},[148],[60,2882,2883,2886],{"style":152},[60,2884],{"className":2885,"style":157},[156],[60,2887,2889],{"className":2888},[161,162,163,164],[60,2890,2892,2895],{"className":2891},[127,164],[60,2893,87],{"className":2894,"style":171},[127,164],[60,2896,2898,2901],{"className":2897},[127,164],[60,2899,359],{"className":2900},[127,178,164],[60,2902,2904],{"className":2903},[183],[60,2905,2907,2927],{"className":2906},[139,140],[60,2908,2910,2924],{"className":2909},[144],[60,2911,2913],{"className":2912,"style":193},[148],[60,2914,2915,2918],{"style":2391},[60,2916],{"className":2917,"style":200},[156],[60,2919,2921],{"className":2920},[161,204,205,164],[60,2922,104],{"className":2923},[127,164],[60,2925,213],{"className":2926},[212],[60,2928,2930],{"className":2929},[144],[60,2931,2933],{"className":2932,"style":220},[148],[60,2934],{},[60,2936,2937,2940],{"style":225},[60,2938],{"className":2939,"style":157},[156],[60,2941],{"className":2942,"style":233},[232],[60,2944,2945,2948],{"style":236},[60,2946],{"className":2947,"style":157},[156],[60,2949,2951],{"className":2950},[161,162,163,164],[60,2952,2954,2957],{"className":2953},[127,164],[60,2955,87],{"className":2956,"style":171},[127,164],[60,2958,90],{"className":2959},[127,178,164],[60,2961,213],{"className":2962},[212],[60,2964,2966],{"className":2965},[144],[60,2967,2970],{"className":2968,"style":2969},[148],"height:0.4451em;",[60,2971],{},[60,2973],{"className":2974},[267,132],[60,2976],{"className":2977,"style":470},[469],[60,2979,448],{"className":2980},[474],[60,2982],{"className":2983,"style":470},[469],[60,2985,2987,2990,2993,2996,2999,3039,3042,3045,3085,3088,3091,3094],{"className":2986},[118],[60,2988],{"className":2989,"style":418},[122],[60,2991,817],{"className":2992},[127],[60,2994,562],{"className":2995,"style":639},[127,178],[60,2997,400],{"className":2998},[131],[60,3000,3002,3005],{"className":3001},[127],[60,3003,359],{"className":3004},[127,178],[60,3006,3008],{"className":3007},[183],[60,3009,3011,3031],{"className":3010},[139,140],[60,3012,3014,3028],{"className":3013},[144],[60,3015,3017],{"className":3016,"style":318},[148],[60,3018,3019,3022],{"style":1940},[60,3020],{"className":3021,"style":325},[156],[60,3023,3025],{"className":3024},[161,162,163,164],[60,3026,104],{"className":3027},[127,164],[60,3029,213],{"className":3030},[212],[60,3032,3034],{"className":3033},[144],[60,3035,3037],{"className":3036,"style":341},[148],[60,3038],{},[60,3040,569],{"className":3041},[649],[60,3043],{"className":3044,"style":653},[469],[60,3046,3048,3051],{"className":3047},[127],[60,3049,100],{"className":3050,"style":179},[127,178],[60,3052,3054],{"className":3053},[183],[60,3055,3057,3077],{"className":3056},[139,140],[60,3058,3060,3074],{"className":3059},[144],[60,3061,3063],{"className":3062,"style":318},[148],[60,3064,3065,3068],{"style":321},[60,3066],{"className":3067,"style":325},[156],[60,3069,3071],{"className":3070},[161,162,163,164],[60,3072,104],{"className":3073},[127,164],[60,3075,213],{"className":3076},[212],[60,3078,3080],{"className":3079},[144],[60,3081,3083],{"className":3082,"style":341},[148],[60,3084],{},[60,3086,405],{"className":3087},[267],[60,3089],{"className":3090,"style":924},[469],[60,3092,2831],{"className":3093},[928],[60,3095],{"className":3096,"style":924},[469],[60,3098,3100,3103],{"className":3099},[118],[60,3101],{"className":3102,"style":123},[122],[60,3104,3106,3109,3211],{"className":3105},[127],[60,3107],{"className":3108},[131,132],[60,3110,3112],{"className":3111},[79],[60,3113,3115,3203],{"className":3114},[139,140],[60,3116,3118,3200],{"className":3117},[144],[60,3119,3121,3175,3183],{"className":3120,"style":149},[148],[60,3122,3123,3126],{"style":152},[60,3124],{"className":3125,"style":157},[156],[60,3127,3129],{"className":3128},[161,162,163,164],[60,3130,3132,3135],{"className":3131},[127,164],[60,3133,87],{"className":3134,"style":171},[127,164],[60,3136,3138,3141],{"className":3137},[127,164],[60,3139,100],{"className":3140,"style":179},[127,178,164],[60,3142,3144],{"className":3143},[183],[60,3145,3147,3167],{"className":3146},[139,140],[60,3148,3150,3164],{"className":3149},[144],[60,3151,3153],{"className":3152,"style":193},[148],[60,3154,3155,3158],{"style":196},[60,3156],{"className":3157,"style":200},[156],[60,3159,3161],{"className":3160},[161,204,205,164],[60,3162,104],{"className":3163},[127,164],[60,3165,213],{"className":3166},[212],[60,3168,3170],{"className":3169},[144],[60,3171,3173],{"className":3172,"style":220},[148],[60,3174],{},[60,3176,3177,3180],{"style":225},[60,3178],{"className":3179,"style":157},[156],[60,3181],{"className":3182,"style":233},[232],[60,3184,3185,3188],{"style":236},[60,3186],{"className":3187,"style":157},[156],[60,3189,3191],{"className":3190},[161,162,163,164],[60,3192,3194,3197],{"className":3193},[127,164],[60,3195,87],{"className":3196,"style":171},[127,164],[60,3198,90],{"className":3199},[127,178,164],[60,3201,213],{"className":3202},[212],[60,3204,3206],{"className":3205},[144],[60,3207,3209],{"className":3208,"style":261},[148],[60,3210],{},[60,3212],{"className":3213},[267,132],[51,3215,3216],{},[33,3217,3218,3220,3221,3290,3291,3360,3361,3505],{},[26,3219,2555],{}," 这个公式很有趣，它其实告诉我们，对 ",[60,3222,3224,3241],{"className":3223},[63],[60,3225,3227],{"className":3226},[67],[69,3228,3229],{"xmlns":71},[73,3230,3231,3239],{},[76,3232,3233],{},[96,3234,3235,3237],{},[84,3236,359],{},[102,3238,104],{},[106,3240,2724],{"encoding":108},[60,3242,3244],{"className":3243,"ariaHidden":114},[113],[60,3245,3247,3250],{"className":3246},[118],[60,3248],{"className":3249,"style":2734},[122],[60,3251,3253,3256],{"className":3252},[127],[60,3254,359],{"className":3255},[127,178],[60,3257,3259],{"className":3258},[183],[60,3260,3262,3282],{"className":3261},[139,140],[60,3263,3265,3279],{"className":3264},[144],[60,3266,3268],{"className":3267,"style":318},[148],[60,3269,3270,3273],{"style":1940},[60,3271],{"className":3272,"style":325},[156],[60,3274,3276],{"className":3275},[161,162,163,164],[60,3277,104],{"className":3278},[127,164],[60,3280,213],{"className":3281},[212],[60,3283,3285],{"className":3284},[144],[60,3286,3288],{"className":3287,"style":341},[148],[60,3289],{}," 的导数可以通过对 ",[60,3292,3294,3311],{"className":3293},[63],[60,3295,3297],{"className":3296},[67],[69,3298,3299],{"xmlns":71},[73,3300,3301,3309],{},[76,3302,3303],{},[96,3304,3305,3307],{},[84,3306,100],{},[102,3308,104],{},[106,3310,289],{"encoding":108},[60,3312,3314],{"className":3313,"ariaHidden":114},[113],[60,3315,3317,3320],{"className":3316},[118],[60,3318],{"className":3319,"style":299},[122],[60,3321,3323,3326],{"className":3322},[127],[60,3324,100],{"className":3325,"style":179},[127,178],[60,3327,3329],{"className":3328},[183],[60,3330,3332,3352],{"className":3331},[139,140],[60,3333,3335,3349],{"className":3334},[144],[60,3336,3338],{"className":3337,"style":318},[148],[60,3339,3340,3343],{"style":321},[60,3341],{"className":3342,"style":325},[156],[60,3344,3346],{"className":3345},[161,162,163,164],[60,3347,104],{"className":3348},[127,164],[60,3350,213],{"className":3351},[212],[60,3353,3355],{"className":3354},[144],[60,3356,3358],{"className":3357,"style":341},[148],[60,3359],{}," 的导数算出来。它多乘了一个 ",[60,3362,3364,3398],{"className":3363},[63],[60,3365,3367],{"className":3366},[67],[69,3368,3369],{"xmlns":71},[73,3370,3371,3395],{},[76,3372,3373,3375,3377,3379,3385,3387,3393],{},[397,3374,817],{},[84,3376,562],{},[397,3378,400],{"stretchy":399},[96,3380,3381,3383],{},[84,3382,359],{},[102,3384,104],{},[397,3386,569],{"separator":114},[96,3388,3389,3391],{},[84,3390,100],{},[102,3392,104],{},[397,3394,405],{"stretchy":399},[106,3396,3397],{"encoding":108},"-f(x_0,y_0)",[60,3399,3401],{"className":3400,"ariaHidden":114},[113],[60,3402,3404,3407,3410,3413,3416,3456,3459,3462,3502],{"className":3403},[118],[60,3405],{"className":3406,"style":418},[122],[60,3408,817],{"className":3409},[127],[60,3411,562],{"className":3412,"style":639},[127,178],[60,3414,400],{"className":3415},[131],[60,3417,3419,3422],{"className":3418},[127],[60,3420,359],{"className":3421},[127,178],[60,3423,3425],{"className":3424},[183],[60,3426,3428,3448],{"className":3427},[139,140],[60,3429,3431,3445],{"className":3430},[144],[60,3432,3434],{"className":3433,"style":318},[148],[60,3435,3436,3439],{"style":1940},[60,3437],{"className":3438,"style":325},[156],[60,3440,3442],{"className":3441},[161,162,163,164],[60,3443,104],{"className":3444},[127,164],[60,3446,213],{"className":3447},[212],[60,3449,3451],{"className":3450},[144],[60,3452,3454],{"className":3453,"style":341},[148],[60,3455],{},[60,3457,569],{"className":3458},[649],[60,3460],{"className":3461,"style":653},[469],[60,3463,3465,3468],{"className":3464},[127],[60,3466,100],{"className":3467,"style":179},[127,178],[60,3469,3471],{"className":3470},[183],[60,3472,3474,3494],{"className":3473},[139,140],[60,3475,3477,3491],{"className":3476},[144],[60,3478,3480],{"className":3479,"style":318},[148],[60,3481,3482,3485],{"style":321},[60,3483],{"className":3484,"style":325},[156],[60,3486,3488],{"className":3487},[161,162,163,164],[60,3489,104],{"className":3490},[127,164],[60,3492,213],{"className":3493},[212],[60,3495,3497],{"className":3496},[144],[60,3498,3500],{"className":3499,"style":341},[148],[60,3501],{},[60,3503,405],{"className":3504},[267],"（即初始处的斜率）。",[15,3507],{},[18,3509,3511],{"id":3510},"第三步构建答案-problem-solving","第三步：构建答案 (Problem Solving)",[23,3513,3514],{},"我将一步步为你讲解这两道题目。",[496,3516,3518],{"id":3517},"题目-1","题目 1",[23,3520,3521,3524,3525,3600,3601,3775,3776,3970,3971,4261,4262,488],{},[26,3522,3523],{},"题目："," 假设 ",[60,3526,3528,3560],{"className":3527},[63],[60,3529,3531],{"className":3530},[67],[69,3532,3533],{"xmlns":71},[73,3534,3535,3557],{},[76,3536,3537,3540,3542,3544,3546,3548,3551,3553,3555],{},[84,3538,3539],{},"P",[397,3541,400],{"stretchy":399},[84,3543,359],{},[397,3545,405],{"stretchy":399},[397,3547,569],{"separator":114},[84,3549,3550],{},"Q",[397,3552,400],{"stretchy":399},[84,3554,359],{},[397,3556,405],{"stretchy":399},[106,3558,3559],{"encoding":108},"P(x), Q(x)",[60,3561,3563],{"className":3562,"ariaHidden":114},[113],[60,3564,3566,3569,3573,3576,3579,3582,3585,3588,3591,3594,3597],{"className":3565},[118],[60,3567],{"className":3568,"style":418},[122],[60,3570,3539],{"className":3571,"style":3572},[127,178],"margin-right:0.1389em;",[60,3574,400],{"className":3575},[131],[60,3577,359],{"className":3578},[127,178],[60,3580,405],{"className":3581},[267],[60,3583,569],{"className":3584},[649],[60,3586],{"className":3587,"style":653},[469],[60,3589,3550],{"className":3590},[127,178],[60,3592,400],{"className":3593},[131],[60,3595,359],{"className":3596},[127,178],[60,3598,405],{"className":3599},[267]," 连续，",[60,3602,3604,3644],{"className":3603},[63],[60,3605,3607],{"className":3606},[67],[69,3608,3609],{"xmlns":71},[73,3610,3611,3641],{},[76,3612,3613,3615,3617,3619,3621,3623,3625,3631,3633,3639],{},[84,3614,100],{},[397,3616,448],{},[84,3618,90],{},[397,3620,400],{"stretchy":399},[84,3622,359],{},[397,3624,569],{"separator":114},[96,3626,3627,3629],{},[84,3628,359],{},[102,3630,104],{},[397,3632,569],{"separator":114},[96,3634,3635,3637],{},[84,3636,100],{},[102,3638,104],{},[397,3640,405],{"stretchy":399},[106,3642,3643],{"encoding":108},"y = \\varphi(x,x_0,y_0)",[60,3645,3647,3665],{"className":3646,"ariaHidden":114},[113],[60,3648,3650,3653,3656,3659,3662],{"className":3649},[118],[60,3651],{"className":3652,"style":299},[122],[60,3654,100],{"className":3655,"style":179},[127,178],[60,3657],{"className":3658,"style":470},[469],[60,3660,448],{"className":3661},[474],[60,3663],{"className":3664,"style":470},[469],[60,3666,3668,3671,3674,3677,3680,3683,3686,3726,3729,3732,3772],{"className":3667},[118],[60,3669],{"className":3670,"style":418},[122],[60,3672,90],{"className":3673},[127,178],[60,3675,400],{"className":3676},[131],[60,3678,359],{"className":3679},[127,178],[60,3681,569],{"className":3682},[649],[60,3684],{"className":3685,"style":653},[469],[60,3687,3689,3692],{"className":3688},[127],[60,3690,359],{"className":3691},[127,178],[60,3693,3695],{"className":3694},[183],[60,3696,3698,3718],{"className":3697},[139,140],[60,3699,3701,3715],{"className":3700},[144],[60,3702,3704],{"className":3703,"style":318},[148],[60,3705,3706,3709],{"style":1940},[60,3707],{"className":3708,"style":325},[156],[60,3710,3712],{"className":3711},[161,162,163,164],[60,3713,104],{"className":3714},[127,164],[60,3716,213],{"className":3717},[212],[60,3719,3721],{"className":3720},[144],[60,3722,3724],{"className":3723,"style":341},[148],[60,3725],{},[60,3727,569],{"className":3728},[649],[60,3730],{"className":3731,"style":653},[469],[60,3733,3735,3738],{"className":3734},[127],[60,3736,100],{"className":3737,"style":179},[127,178],[60,3739,3741],{"className":3740},[183],[60,3742,3744,3764],{"className":3743},[139,140],[60,3745,3747,3761],{"className":3746},[144],[60,3748,3750],{"className":3749,"style":318},[148],[60,3751,3752,3755],{"style":321},[60,3753],{"className":3754,"style":325},[156],[60,3756,3758],{"className":3757},[161,162,163,164],[60,3759,104],{"className":3760},[127,164],[60,3762,213],{"className":3763},[212],[60,3765,3767],{"className":3766},[144],[60,3768,3770],{"className":3769,"style":341},[148],[60,3771],{},[60,3773,405],{"className":3774},[267]," 是方程 ",[60,3777,3779,3827],{"className":3778},[63],[60,3780,3782],{"className":3781},[67],[69,3783,3784],{"xmlns":71},[73,3785,3786,3824],{},[76,3787,3788,3802,3804,3806,3808,3810,3812,3814,3816,3818,3820,3822],{},[79,3789,3790,3796],{},[76,3791,3792,3794],{},[84,3793,2173],{"mathvariant":86},[84,3795,100],{},[76,3797,3798,3800],{},[84,3799,2173],{"mathvariant":86},[84,3801,359],{},[397,3803,448],{},[84,3805,3539],{},[397,3807,400],{"stretchy":399},[84,3809,359],{},[397,3811,405],{"stretchy":399},[84,3813,100],{},[397,3815,990],{},[84,3817,3550],{},[397,3819,400],{"stretchy":399},[84,3821,359],{},[397,3823,405],{"stretchy":399},[106,3825,3826],{"encoding":108},"\\frac{\\mathrm{d}y}{\\mathrm{d}x} = P(x)y + Q(x)",[60,3828,3830,3922,3952],{"className":3829,"ariaHidden":114},[113],[60,3831,3833,3837,3913,3916,3919],{"className":3832},[118],[60,3834],{"className":3835,"style":3836},[122],"height:1.2772em;vertical-align:-0.345em;",[60,3838,3840,3843,3910],{"className":3839},[127],[60,3841],{"className":3842},[131,132],[60,3844,3846],{"className":3845},[79],[60,3847,3849,3901],{"className":3848},[139,140],[60,3850,3852,3898],{"className":3851},[144],[60,3853,3855,3873,3881],{"className":3854,"style":149},[148],[60,3856,3857,3860],{"style":152},[60,3858],{"className":3859,"style":157},[156],[60,3861,3863],{"className":3862},[161,162,163,164],[60,3864,3866,3870],{"className":3865},[127,164],[60,3867,2173],{"className":3868},[127,3869,164],"mathrm",[60,3871,359],{"className":3872},[127,178,164],[60,3874,3875,3878],{"style":225},[60,3876],{"className":3877,"style":157},[156],[60,3879],{"className":3880,"style":233},[232],[60,3882,3883,3886],{"style":236},[60,3884],{"className":3885,"style":157},[156],[60,3887,3889],{"className":3888},[161,162,163,164],[60,3890,3892,3895],{"className":3891},[127,164],[60,3893,2173],{"className":3894},[127,3869,164],[60,3896,100],{"className":3897,"style":179},[127,178,164],[60,3899,213],{"className":3900},[212],[60,3902,3904],{"className":3903},[144],[60,3905,3908],{"className":3906,"style":3907},[148],"height:0.345em;",[60,3909],{},[60,3911],{"className":3912},[267,132],[60,3914],{"className":3915,"style":470},[469],[60,3917,448],{"className":3918},[474],[60,3920],{"className":3921,"style":470},[469],[60,3923,3925,3928,3931,3934,3937,3940,3943,3946,3949],{"className":3924},[118],[60,3926],{"className":3927,"style":418},[122],[60,3929,3539],{"className":3930,"style":3572},[127,178],[60,3932,400],{"className":3933},[131],[60,3935,359],{"className":3936},[127,178],[60,3938,405],{"className":3939},[267],[60,3941,100],{"className":3942,"style":179},[127,178],[60,3944],{"className":3945,"style":924},[469],[60,3947,990],{"className":3948},[928],[60,3950],{"className":3951,"style":924},[469],[60,3953,3955,3958,3961,3964,3967],{"className":3954},[118],[60,3956],{"className":3957,"style":418},[122],[60,3959,3550],{"className":3960},[127,178],[60,3962,400],{"className":3963},[131],[60,3965,359],{"className":3966},[127,178],[60,3968,405],{"className":3969},[267]," 的解。求 ",[60,3972,3974,4024],{"className":3973},[63],[60,3975,3977],{"className":3976},[67],[69,3978,3979],{"xmlns":71},[73,3980,3981,4021],{},[76,3982,3983,4001,4003],{},[79,3984,3985,3991],{},[76,3986,3987,3989],{},[84,3988,87],{"mathvariant":86},[84,3990,90],{},[76,3992,3993,3995],{},[84,3994,87],{"mathvariant":86},[96,3996,3997,3999],{},[84,3998,359],{},[102,4000,104],{},[397,4002,569],{"separator":114},[79,4004,4005,4011],{},[76,4006,4007,4009],{},[84,4008,87],{"mathvariant":86},[84,4010,90],{},[76,4012,4013,4015],{},[84,4014,87],{"mathvariant":86},[96,4016,4017,4019],{},[84,4018,100],{},[102,4020,104],{},[106,4022,4023],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial x_0}, \\frac{\\partial \\varphi}{\\partial y_0}",[60,4025,4027],{"className":4026,"ariaHidden":114},[113],[60,4028,4030,4033,4144,4147,4150],{"className":4029},[118],[60,4031],{"className":4032,"style":123},[122],[60,4034,4036,4039,4141],{"className":4035},[127],[60,4037],{"className":4038},[131,132],[60,4040,4042],{"className":4041},[79],[60,4043,4045,4133],{"className":4044},[139,140],[60,4046,4048,4130],{"className":4047},[144],[60,4049,4051,4105,4113],{"className":4050,"style":149},[148],[60,4052,4053,4056],{"style":152},[60,4054],{"className":4055,"style":157},[156],[60,4057,4059],{"className":4058},[161,162,163,164],[60,4060,4062,4065],{"className":4061},[127,164],[60,4063,87],{"className":4064,"style":171},[127,164],[60,4066,4068,4071],{"className":4067},[127,164],[60,4069,359],{"className":4070},[127,178,164],[60,4072,4074],{"className":4073},[183],[60,4075,4077,4097],{"className":4076},[139,140],[60,4078,4080,4094],{"className":4079},[144],[60,4081,4083],{"className":4082,"style":193},[148],[60,4084,4085,4088],{"style":2391},[60,4086],{"className":4087,"style":200},[156],[60,4089,4091],{"className":4090},[161,204,205,164],[60,4092,104],{"className":4093},[127,164],[60,4095,213],{"className":4096},[212],[60,4098,4100],{"className":4099},[144],[60,4101,4103],{"className":4102,"style":220},[148],[60,4104],{},[60,4106,4107,4110],{"style":225},[60,4108],{"className":4109,"style":157},[156],[60,4111],{"className":4112,"style":233},[232],[60,4114,4115,4118],{"style":236},[60,4116],{"className":4117,"style":157},[156],[60,4119,4121],{"className":4120},[161,162,163,164],[60,4122,4124,4127],{"className":4123},[127,164],[60,4125,87],{"className":4126,"style":171},[127,164],[60,4128,90],{"className":4129},[127,178,164],[60,4131,213],{"className":4132},[212],[60,4134,4136],{"className":4135},[144],[60,4137,4139],{"className":4138,"style":2969},[148],[60,4140],{},[60,4142],{"className":4143},[267,132],[60,4145,569],{"className":4146},[649],[60,4148],{"className":4149,"style":653},[469],[60,4151,4153,4156,4258],{"className":4152},[127],[60,4154],{"className":4155},[131,132],[60,4157,4159],{"className":4158},[79],[60,4160,4162,4250],{"className":4161},[139,140],[60,4163,4165,4247],{"className":4164},[144],[60,4166,4168,4222,4230],{"className":4167,"style":149},[148],[60,4169,4170,4173],{"style":152},[60,4171],{"className":4172,"style":157},[156],[60,4174,4176],{"className":4175},[161,162,163,164],[60,4177,4179,4182],{"className":4178},[127,164],[60,4180,87],{"className":4181,"style":171},[127,164],[60,4183,4185,4188],{"className":4184},[127,164],[60,4186,100],{"className":4187,"style":179},[127,178,164],[60,4189,4191],{"className":4190},[183],[60,4192,4194,4214],{"className":4193},[139,140],[60,4195,4197,4211],{"className":4196},[144],[60,4198,4200],{"className":4199,"style":193},[148],[60,4201,4202,4205],{"style":196},[60,4203],{"className":4204,"style":200},[156],[60,4206,4208],{"className":4207},[161,204,205,164],[60,4209,104],{"className":4210},[127,164],[60,4212,213],{"className":4213},[212],[60,4215,4217],{"className":4216},[144],[60,4218,4220],{"className":4219,"style":220},[148],[60,4221],{},[60,4223,4224,4227],{"style":225},[60,4225],{"className":4226,"style":157},[156],[60,4228],{"className":4229,"style":233},[232],[60,4231,4232,4235],{"style":236},[60,4233],{"className":4234,"style":157},[156],[60,4236,4238],{"className":4237},[161,162,163,164],[60,4239,4241,4244],{"className":4240},[127,164],[60,4242,87],{"className":4243,"style":171},[127,164],[60,4245,90],{"className":4246},[127,178,164],[60,4248,213],{"className":4249},[212],[60,4251,4253],{"className":4252},[144],[60,4254,4256],{"className":4255,"style":261},[148],[60,4257],{},[60,4259],{"className":4260},[267,132]," 及 ",[60,4263,4265,4291],{"className":4264},[63],[60,4266,4268],{"className":4267},[67],[69,4269,4270],{"xmlns":71},[73,4271,4272,4288],{},[76,4273,4274],{},[79,4275,4276,4282],{},[76,4277,4278,4280],{},[84,4279,87],{"mathvariant":86},[84,4281,90],{},[76,4283,4284,4286],{},[84,4285,87],{"mathvariant":86},[84,4287,359],{},[106,4289,4290],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial x}",[60,4292,4294],{"className":4293,"ariaHidden":114},[113],[60,4295,4297,4300],{"className":4296},[118],[60,4298],{"className":4299,"style":3836},[122],[60,4301,4303,4306,4371],{"className":4302},[127],[60,4304],{"className":4305},[131,132],[60,4307,4309],{"className":4308},[79],[60,4310,4312,4363],{"className":4311},[139,140],[60,4313,4315,4360],{"className":4314},[144],[60,4316,4318,4335,4343],{"className":4317,"style":149},[148],[60,4319,4320,4323],{"style":152},[60,4321],{"className":4322,"style":157},[156],[60,4324,4326],{"className":4325},[161,162,163,164],[60,4327,4329,4332],{"className":4328},[127,164],[60,4330,87],{"className":4331,"style":171},[127,164],[60,4333,359],{"className":4334},[127,178,164],[60,4336,4337,4340],{"style":225},[60,4338],{"className":4339,"style":157},[156],[60,4341],{"className":4342,"style":233},[232],[60,4344,4345,4348],{"style":236},[60,4346],{"className":4347,"style":157},[156],[60,4349,4351],{"className":4350},[161,162,163,164],[60,4352,4354,4357],{"className":4353},[127,164],[60,4355,87],{"className":4356,"style":171},[127,164],[60,4358,90],{"className":4359},[127,178,164],[60,4361,213],{"className":4362},[212],[60,4364,4366],{"className":4365},[144],[60,4367,4369],{"className":4368,"style":3907},[148],[60,4370],{},[60,4372],{"className":4373},[267,132],[23,4375,4376],{},[26,4377,4378],{},"详细解析：",[23,4380,4381,4442,4443,4633,4634,4770,4771,4799,4800,4828,4829,4940,4941],{},[26,4382,4383,4384,4441],{},"Step 1: 识别 ",[60,4385,4387,4411],{"className":4386},[63],[60,4388,4390],{"className":4389},[67],[69,4391,4392],{"xmlns":71},[73,4393,4394,4408],{},[76,4395,4396,4398,4400,4402,4404,4406],{},[84,4397,562],{},[397,4399,400],{"stretchy":399},[84,4401,359],{},[397,4403,569],{"separator":114},[84,4405,100],{},[397,4407,405],{"stretchy":399},[106,4409,4410],{"encoding":108},"f(x,y)",[60,4412,4414],{"className":4413,"ariaHidden":114},[113],[60,4415,4417,4420,4423,4426,4429,4432,4435,4438],{"className":4416},[118],[60,4418],{"className":4419,"style":418},[122],[60,4421,562],{"className":4422,"style":639},[127,178],[60,4424,400],{"className":4425},[131],[60,4427,359],{"className":4428},[127,178],[60,4430,569],{"className":4431},[649],[60,4433],{"className":4434,"style":653},[469],[60,4436,100],{"className":4437,"style":179},[127,178],[60,4439,405],{"className":4440},[267]," 及其偏导数","\n根据方程 ",[60,4444,4446,4493],{"className":4445},[63],[60,4447,4449],{"className":4448},[67],[69,4450,4451],{"xmlns":71},[73,4452,4453,4491],{},[76,4454,4455,4469,4471,4473,4475,4477,4479,4481,4483,4485,4487,4489],{},[79,4456,4457,4463],{},[76,4458,4459,4461],{},[84,4460,2173],{"mathvariant":86},[84,4462,100],{},[76,4464,4465,4467],{},[84,4466,2173],{"mathvariant":86},[84,4468,359],{},[397,4470,448],{},[84,4472,3539],{},[397,4474,400],{"stretchy":399},[84,4476,359],{},[397,4478,405],{"stretchy":399},[84,4480,100],{},[397,4482,990],{},[84,4484,3550],{},[397,4486,400],{"stretchy":399},[84,4488,359],{},[397,4490,405],{"stretchy":399},[106,4492,3826],{"encoding":108},[60,4494,4496,4585,4615],{"className":4495,"ariaHidden":114},[113],[60,4497,4499,4502,4576,4579,4582],{"className":4498},[118],[60,4500],{"className":4501,"style":3836},[122],[60,4503,4505,4508,4573],{"className":4504},[127],[60,4506],{"className":4507},[131,132],[60,4509,4511],{"className":4510},[79],[60,4512,4514,4565],{"className":4513},[139,140],[60,4515,4517,4562],{"className":4516},[144],[60,4518,4520,4537,4545],{"className":4519,"style":149},[148],[60,4521,4522,4525],{"style":152},[60,4523],{"className":4524,"style":157},[156],[60,4526,4528],{"className":4527},[161,162,163,164],[60,4529,4531,4534],{"className":4530},[127,164],[60,4532,2173],{"className":4533},[127,3869,164],[60,4535,359],{"className":4536},[127,178,164],[60,4538,4539,4542],{"style":225},[60,4540],{"className":4541,"style":157},[156],[60,4543],{"className":4544,"style":233},[232],[60,4546,4547,4550],{"style":236},[60,4548],{"className":4549,"style":157},[156],[60,4551,4553],{"className":4552},[161,162,163,164],[60,4554,4556,4559],{"className":4555},[127,164],[60,4557,2173],{"className":4558},[127,3869,164],[60,4560,100],{"className":4561,"style":179},[127,178,164],[60,4563,213],{"className":4564},[212],[60,4566,4568],{"className":4567},[144],[60,4569,4571],{"className":4570,"style":3907},[148],[60,4572],{},[60,4574],{"className":4575},[267,132],[60,4577],{"className":4578,"style":470},[469],[60,4580,448],{"className":4581},[474],[60,4583],{"className":4584,"style":470},[469],[60,4586,4588,4591,4594,4597,4600,4603,4606,4609,4612],{"className":4587},[118],[60,4589],{"className":4590,"style":418},[122],[60,4592,3539],{"className":4593,"style":3572},[127,178],[60,4595,400],{"className":4596},[131],[60,4598,359],{"className":4599},[127,178],[60,4601,405],{"className":4602},[267],[60,4604,100],{"className":4605,"style":179},[127,178],[60,4607],{"className":4608,"style":924},[469],[60,4610,990],{"className":4611},[928],[60,4613],{"className":4614,"style":924},[469],[60,4616,4618,4621,4624,4627,4630],{"className":4617},[118],[60,4619],{"className":4620,"style":418},[122],[60,4622,3550],{"className":4623},[127,178],[60,4625,400],{"className":4626},[131],[60,4628,359],{"className":4629},[127,178],[60,4631,405],{"className":4632},[267],"，我们可以确定右端函数为：\n",[60,4635,4637,4683],{"className":4636},[63],[60,4638,4640],{"className":4639},[67],[69,4641,4642],{"xmlns":71},[73,4643,4644,4680],{},[76,4645,4646,4648,4650,4652,4654,4656,4658,4660,4662,4664,4666,4668,4670,4672,4674,4676,4678],{},[84,4647,562],{},[397,4649,400],{"stretchy":399},[84,4651,359],{},[397,4653,569],{"separator":114},[84,4655,100],{},[397,4657,405],{"stretchy":399},[397,4659,448],{},[84,4661,3539],{},[397,4663,400],{"stretchy":399},[84,4665,359],{},[397,4667,405],{"stretchy":399},[84,4669,100],{},[397,4671,990],{},[84,4673,3550],{},[397,4675,400],{"stretchy":399},[84,4677,359],{},[397,4679,405],{"stretchy":399},[106,4681,4682],{"encoding":108},"f(x,y) = P(x)y + Q(x)",[60,4684,4686,4722,4752],{"className":4685,"ariaHidden":114},[113],[60,4687,4689,4692,4695,4698,4701,4704,4707,4710,4713,4716,4719],{"className":4688},[118],[60,4690],{"className":4691,"style":418},[122],[60,4693,562],{"className":4694,"style":639},[127,178],[60,4696,400],{"className":4697},[131],[60,4699,359],{"className":4700},[127,178],[60,4702,569],{"className":4703},[649],[60,4705],{"className":4706,"style":653},[469],[60,4708,100],{"className":4709,"style":179},[127,178],[60,4711,405],{"className":4712},[267],[60,4714],{"className":4715,"style":470},[469],[60,4717,448],{"className":4718},[474],[60,4720],{"className":4721,"style":470},[469],[60,4723,4725,4728,4731,4734,4737,4740,4743,4746,4749],{"className":4724},[118],[60,4726],{"className":4727,"style":418},[122],[60,4729,3539],{"className":4730,"style":3572},[127,178],[60,4732,400],{"className":4733},[131],[60,4735,359],{"className":4736},[127,178],[60,4738,405],{"className":4739},[267],[60,4741,100],{"className":4742,"style":179},[127,178],[60,4744],{"className":4745,"style":924},[469],[60,4747,990],{"className":4748},[928],[60,4750],{"className":4751,"style":924},[469],[60,4753,4755,4758,4761,4764,4767],{"className":4754},[118],[60,4756],{"className":4757,"style":418},[122],[60,4759,3550],{"className":4760},[127,178],[60,4762,400],{"className":4763},[131],[60,4765,359],{"className":4766},[127,178],[60,4768,405],{"className":4769},[267],"\n我们需要计算 ",[60,4772,4774,4787],{"className":4773},[63],[60,4775,4777],{"className":4776},[67],[69,4778,4779],{"xmlns":71},[73,4780,4781,4785],{},[76,4782,4783],{},[84,4784,562],{},[106,4786,562],{"encoding":108},[60,4788,4790],{"className":4789,"ariaHidden":114},[113],[60,4791,4793,4796],{"className":4792},[118],[60,4794],{"className":4795,"style":694},[122],[60,4797,562],{"className":4798,"style":639},[127,178]," 对 ",[60,4801,4803,4816],{"className":4802},[63],[60,4804,4806],{"className":4805},[67],[69,4807,4808],{"xmlns":71},[73,4809,4810,4814],{},[76,4811,4812],{},[84,4813,100],{},[106,4815,100],{"encoding":108},[60,4817,4819],{"className":4818,"ariaHidden":114},[113],[60,4820,4822,4825],{"className":4821},[118],[60,4823],{"className":4824,"style":299},[122],[60,4826,100],{"className":4827,"style":179},[127,178]," 的偏导数 ",[60,4830,4832,4857],{"className":4831},[63],[60,4833,4835],{"className":4834},[67],[69,4836,4837],{"xmlns":71},[73,4838,4839,4855],{},[76,4840,4841],{},[79,4842,4843,4849],{},[76,4844,4845,4847],{},[84,4846,87],{"mathvariant":86},[84,4848,562],{},[76,4850,4851,4853],{},[84,4852,87],{"mathvariant":86},[84,4854,100],{},[106,4856,2585],{"encoding":108},[60,4858,4860],{"className":4859,"ariaHidden":114},[113],[60,4861,4863,4866],{"className":4862},[118],[60,4864],{"className":4865,"style":123},[122],[60,4867,4869,4872,4937],{"className":4868},[127],[60,4870],{"className":4871},[131,132],[60,4873,4875],{"className":4874},[79],[60,4876,4878,4929],{"className":4877},[139,140],[60,4879,4881,4926],{"className":4880},[144],[60,4882,4884,4901,4909],{"className":4883,"style":149},[148],[60,4885,4886,4889],{"style":152},[60,4887],{"className":4888,"style":157},[156],[60,4890,4892],{"className":4891},[161,162,163,164],[60,4893,4895,4898],{"className":4894},[127,164],[60,4896,87],{"className":4897,"style":171},[127,164],[60,4899,100],{"className":4900,"style":179},[127,178,164],[60,4902,4903,4906],{"style":225},[60,4904],{"className":4905,"style":157},[156],[60,4907],{"className":4908,"style":233},[232],[60,4910,4911,4914],{"style":236},[60,4912],{"className":4913,"style":157},[156],[60,4915,4917],{"className":4916},[161,162,163,164],[60,4918,4920,4923],{"className":4919},[127,164],[60,4921,87],{"className":4922,"style":171},[127,164],[60,4924,562],{"className":4925,"style":639},[127,178,164],[60,4927,213],{"className":4928},[212],[60,4930,4932],{"className":4931},[144],[60,4933,4935],{"className":4934,"style":261},[148],[60,4936],{},[60,4938],{"className":4939},[267,132],"，这是使用定理5公式的关键：\n",[60,4942,4944,5018],{"className":4943},[63],[60,4945,4947],{"className":4946},[67],[69,4948,4949],{"xmlns":71},[73,4950,4951,5015],{},[76,4952,4953,4967,4969,4979,4982,4984,4986,4988,4990,4992,4994,4996,4998,5000,5002,5005,5007,5009,5011,5013],{},[79,4954,4955,4961],{},[76,4956,4957,4959],{},[84,4958,87],{"mathvariant":86},[84,4960,562],{},[76,4962,4963,4965],{},[84,4964,87],{"mathvariant":86},[84,4966,100],{},[397,4968,448],{},[79,4970,4971,4973],{},[84,4972,87],{"mathvariant":86},[76,4974,4975,4977],{},[84,4976,87],{"mathvariant":86},[84,4978,100],{},[397,4980,4981],{"stretchy":399},"[",[84,4983,3539],{},[397,4985,400],{"stretchy":399},[84,4987,359],{},[397,4989,405],{"stretchy":399},[84,4991,100],{},[397,4993,990],{},[84,4995,3550],{},[397,4997,400],{"stretchy":399},[84,4999,359],{},[397,5001,405],{"stretchy":399},[397,5003,5004],{"stretchy":399},"]",[397,5006,448],{},[84,5008,3539],{},[397,5010,400],{"stretchy":399},[84,5012,359],{},[397,5014,405],{"stretchy":399},[106,5016,5017],{"encoding":108},"\\frac{\\partial f}{\\partial y} = \\frac{\\partial}{\\partial y} [P(x)y + Q(x)] = P(x)",[60,5019,5021,5110,5216,5244],{"className":5020,"ariaHidden":114},[113],[60,5022,5024,5027,5101,5104,5107],{"className":5023},[118],[60,5025],{"className":5026,"style":123},[122],[60,5028,5030,5033,5098],{"className":5029},[127],[60,5031],{"className":5032},[131,132],[60,5034,5036],{"className":5035},[79],[60,5037,5039,5090],{"className":5038},[139,140],[60,5040,5042,5087],{"className":5041},[144],[60,5043,5045,5062,5070],{"className":5044,"style":149},[148],[60,5046,5047,5050],{"style":152},[60,5048],{"className":5049,"style":157},[156],[60,5051,5053],{"className":5052},[161,162,163,164],[60,5054,5056,5059],{"className":5055},[127,164],[60,5057,87],{"className":5058,"style":171},[127,164],[60,5060,100],{"className":5061,"style":179},[127,178,164],[60,5063,5064,5067],{"style":225},[60,5065],{"className":5066,"style":157},[156],[60,5068],{"className":5069,"style":233},[232],[60,5071,5072,5075],{"style":236},[60,5073],{"className":5074,"style":157},[156],[60,5076,5078],{"className":5077},[161,162,163,164],[60,5079,5081,5084],{"className":5080},[127,164],[60,5082,87],{"className":5083,"style":171},[127,164],[60,5085,562],{"className":5086,"style":639},[127,178,164],[60,5088,213],{"className":5089},[212],[60,5091,5093],{"className":5092},[144],[60,5094,5096],{"className":5095,"style":261},[148],[60,5097],{},[60,5099],{"className":5100},[267,132],[60,5102],{"className":5103,"style":470},[469],[60,5105,448],{"className":5106},[474],[60,5108],{"className":5109,"style":470},[469],[60,5111,5113,5117,5189,5192,5195,5198,5201,5204,5207,5210,5213],{"className":5112},[118],[60,5114],{"className":5115,"style":5116},[122],"height:1.3612em;vertical-align:-0.4811em;",[60,5118,5120,5123,5186],{"className":5119},[127],[60,5121],{"className":5122},[131,132],[60,5124,5126],{"className":5125},[79],[60,5127,5129,5178],{"className":5128},[139,140],[60,5130,5132,5175],{"className":5131},[144],[60,5133,5136,5153,5161],{"className":5134,"style":5135},[148],"height:0.8801em;",[60,5137,5138,5141],{"style":152},[60,5139],{"className":5140,"style":157},[156],[60,5142,5144],{"className":5143},[161,162,163,164],[60,5145,5147,5150],{"className":5146},[127,164],[60,5148,87],{"className":5149,"style":171},[127,164],[60,5151,100],{"className":5152,"style":179},[127,178,164],[60,5154,5155,5158],{"style":225},[60,5156],{"className":5157,"style":157},[156],[60,5159],{"className":5160,"style":233},[232],[60,5162,5163,5166],{"style":1105},[60,5164],{"className":5165,"style":157},[156],[60,5167,5169],{"className":5168},[161,162,163,164],[60,5170,5172],{"className":5171},[127,164],[60,5173,87],{"className":5174,"style":171},[127,164],[60,5176,213],{"className":5177},[212],[60,5179,5181],{"className":5180},[144],[60,5182,5184],{"className":5183,"style":261},[148],[60,5185],{},[60,5187],{"className":5188},[267,132],[60,5190,4981],{"className":5191},[131],[60,5193,3539],{"className":5194,"style":3572},[127,178],[60,5196,400],{"className":5197},[131],[60,5199,359],{"className":5200},[127,178],[60,5202,405],{"className":5203},[267],[60,5205,100],{"className":5206,"style":179},[127,178],[60,5208],{"className":5209,"style":924},[469],[60,5211,990],{"className":5212},[928],[60,5214],{"className":5215,"style":924},[469],[60,5217,5219,5222,5225,5228,5231,5235,5238,5241],{"className":5218},[118],[60,5220],{"className":5221,"style":418},[122],[60,5223,3550],{"className":5224},[127,178],[60,5226,400],{"className":5227},[131],[60,5229,359],{"className":5230},[127,178],[60,5232,5234],{"className":5233},[267],")]",[60,5236],{"className":5237,"style":470},[469],[60,5239,448],{"className":5240},[474],[60,5242],{"className":5243,"style":470},[469],[60,5245,5247,5250,5253,5256,5259],{"className":5246},[118],[60,5248],{"className":5249,"style":418},[122],[60,5251,3539],{"className":5252,"style":3572},[127,178],[60,5254,400],{"className":5255},[131],[60,5257,359],{"className":5258},[127,178],[60,5260,405],{"className":5261},[267],[23,5263,5264,5420,5421,5826,5827,5976,5977,6006,6007,6345],{},[26,5265,5266,5267,5419],{},"Step 2: 计算 ",[60,5268,5270,5299],{"className":5269},[63],[60,5271,5273],{"className":5272},[67],[69,5274,5275],{"xmlns":71},[73,5276,5277,5297],{},[76,5278,5279],{},[79,5280,5281,5287],{},[76,5282,5283,5285],{},[84,5284,87],{"mathvariant":86},[84,5286,90],{},[76,5288,5289,5291],{},[84,5290,87],{"mathvariant":86},[96,5292,5293,5295],{},[84,5294,100],{},[102,5296,104],{},[106,5298,109],{"encoding":108},[60,5300,5302],{"className":5301,"ariaHidden":114},[113],[60,5303,5305,5308],{"className":5304},[118],[60,5306],{"className":5307,"style":123},[122],[60,5309,5311,5314,5416],{"className":5310},[127],[60,5312],{"className":5313},[131,132],[60,5315,5317],{"className":5316},[79],[60,5318,5320,5408],{"className":5319},[139,140],[60,5321,5323,5405],{"className":5322},[144],[60,5324,5326,5380,5388],{"className":5325,"style":149},[148],[60,5327,5328,5331],{"style":152},[60,5329],{"className":5330,"style":157},[156],[60,5332,5334],{"className":5333},[161,162,163,164],[60,5335,5337,5340],{"className":5336},[127,164],[60,5338,87],{"className":5339,"style":171},[127,164],[60,5341,5343,5346],{"className":5342},[127,164],[60,5344,100],{"className":5345,"style":179},[127,178,164],[60,5347,5349],{"className":5348},[183],[60,5350,5352,5372],{"className":5351},[139,140],[60,5353,5355,5369],{"className":5354},[144],[60,5356,5358],{"className":5357,"style":193},[148],[60,5359,5360,5363],{"style":196},[60,5361],{"className":5362,"style":200},[156],[60,5364,5366],{"className":5365},[161,204,205,164],[60,5367,104],{"className":5368},[127,164],[60,5370,213],{"className":5371},[212],[60,5373,5375],{"className":5374},[144],[60,5376,5378],{"className":5377,"style":220},[148],[60,5379],{},[60,5381,5382,5385],{"style":225},[60,5383],{"className":5384,"style":157},[156],[60,5386],{"className":5387,"style":233},[232],[60,5389,5390,5393],{"style":236},[60,5391],{"className":5392,"style":157},[156],[60,5394,5396],{"className":5395},[161,162,163,164],[60,5397,5399,5402],{"className":5398},[127,164],[60,5400,87],{"className":5401,"style":171},[127,164],[60,5403,90],{"className":5404},[127,178,164],[60,5406,213],{"className":5407},[212],[60,5409,5411],{"className":5410},[144],[60,5412,5414],{"className":5413,"style":261},[148],[60,5415],{},[60,5417],{"className":5418},[267,132]," (利用公式 3.18)","\n根据公式：\n",[60,5422,5424,5496],{"className":5423},[63],[60,5425,5427],{"className":5426},[67],[69,5428,5429],{"xmlns":71},[73,5430,5431,5493],{},[76,5432,5433,5451,5453,5455,5457],{},[79,5434,5435,5441],{},[76,5436,5437,5439],{},[84,5438,87],{"mathvariant":86},[84,5440,90],{},[76,5442,5443,5445],{},[84,5444,87],{"mathvariant":86},[96,5446,5447,5449],{},[84,5448,100],{},[102,5450,104],{},[397,5452,448],{},[84,5454,2119],{},[397,5456,1465],{},[76,5458,5459,5461,5473,5487,5489,5491],{},[397,5460,400],{"fence":114},[2127,5462,5463,5465,5471],{},[397,5464,2131],{},[96,5466,5467,5469],{},[84,5468,359],{},[102,5470,104],{},[84,5472,359],{},[79,5474,5475,5481],{},[76,5476,5477,5479],{},[84,5478,87],{"mathvariant":86},[84,5480,562],{},[76,5482,5483,5485],{},[84,5484,87],{"mathvariant":86},[84,5486,100],{},[84,5488,2173],{},[84,5490,2152],{},[397,5492,405],{"fence":114},[106,5494,5495],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial y_0} = \\exp\\left( \\int_{x_0}^x \\frac{\\partial f}{\\partial y} dt \\right)",[60,5497,5499,5625],{"className":5498,"ariaHidden":114},[113],[60,5500,5502,5505,5616,5619,5622],{"className":5501},[118],[60,5503],{"className":5504,"style":123},[122],[60,5506,5508,5511,5613],{"className":5507},[127],[60,5509],{"className":5510},[131,132],[60,5512,5514],{"className":5513},[79],[60,5515,5517,5605],{"className":5516},[139,140],[60,5518,5520,5602],{"className":5519},[144],[60,5521,5523,5577,5585],{"className":5522,"style":149},[148],[60,5524,5525,5528],{"style":152},[60,5526],{"className":5527,"style":157},[156],[60,5529,5531],{"className":5530},[161,162,163,164],[60,5532,5534,5537],{"className":5533},[127,164],[60,5535,87],{"className":5536,"style":171},[127,164],[60,5538,5540,5543],{"className":5539},[127,164],[60,5541,100],{"className":5542,"style":179},[127,178,164],[60,5544,5546],{"className":5545},[183],[60,5547,5549,5569],{"className":5548},[139,140],[60,5550,5552,5566],{"className":5551},[144],[60,5553,5555],{"className":5554,"style":193},[148],[60,5556,5557,5560],{"style":196},[60,5558],{"className":5559,"style":200},[156],[60,5561,5563],{"className":5562},[161,204,205,164],[60,5564,104],{"className":5565},[127,164],[60,5567,213],{"className":5568},[212],[60,5570,5572],{"className":5571},[144],[60,5573,5575],{"className":5574,"style":220},[148],[60,5576],{},[60,5578,5579,5582],{"style":225},[60,5580],{"className":5581,"style":157},[156],[60,5583],{"className":5584,"style":233},[232],[60,5586,5587,5590],{"style":236},[60,5588],{"className":5589,"style":157},[156],[60,5591,5593],{"className":5592},[161,162,163,164],[60,5594,5596,5599],{"className":5595},[127,164],[60,5597,87],{"className":5598,"style":171},[127,164],[60,5600,90],{"className":5601},[127,178,164],[60,5603,213],{"className":5604},[212],[60,5606,5608],{"className":5607},[144],[60,5609,5611],{"className":5610,"style":261},[148],[60,5612],{},[60,5614],{"className":5615},[267,132],[60,5617],{"className":5618,"style":470},[469],[60,5620,448],{"className":5621},[474],[60,5623],{"className":5624,"style":470},[469],[60,5626,5628,5631,5634,5637],{"className":5627},[118],[60,5629],{"className":5630,"style":2316},[122],[60,5632,2119],{"className":5633},[1495],[60,5635],{"className":5636,"style":653},[469],[60,5638,5640,5646,5737,5740,5814,5817,5820],{"className":5639},[2326],[60,5641,5643],{"className":5642,"style":2331},[131,2330],[60,5644,400],{"className":5645},[2335,2336],[60,5647,5649,5652],{"className":5648},[1495],[60,5650,2131],{"className":5651,"style":2345},[1495,2343,2344],[60,5653,5655],{"className":5654},[183],[60,5656,5658,5729],{"className":5657},[139,140],[60,5659,5661,5726],{"className":5660},[144],[60,5662,5664,5715],{"className":5663,"style":2358},[148],[60,5665,5666,5669],{"style":2361},[60,5667],{"className":5668,"style":325},[156],[60,5670,5672],{"className":5671},[161,162,163,164],[60,5673,5675],{"className":5674},[127,164],[60,5676,5678,5681],{"className":5677},[127,164],[60,5679,359],{"className":5680},[127,178,164],[60,5682,5684],{"className":5683},[183],[60,5685,5687,5707],{"className":5686},[139,140],[60,5688,5690,5704],{"className":5689},[144],[60,5691,5693],{"className":5692,"style":193},[148],[60,5694,5695,5698],{"style":2391},[60,5696],{"className":5697,"style":200},[156],[60,5699,5701],{"className":5700},[161,204,205,164],[60,5702,104],{"className":5703},[127,164],[60,5705,213],{"className":5706},[212],[60,5708,5710],{"className":5709},[144],[60,5711,5713],{"className":5712,"style":220},[148],[60,5714],{},[60,5716,5717,5720],{"style":2414},[60,5718],{"className":5719,"style":325},[156],[60,5721,5723],{"className":5722},[161,162,163,164],[60,5724,359],{"className":5725},[127,178,164],[60,5727,213],{"className":5728},[212],[60,5730,5732],{"className":5731},[144],[60,5733,5735],{"className":5734,"style":2433},[148],[60,5736],{},[60,5738],{"className":5739,"style":653},[469],[60,5741,5743,5746,5811],{"className":5742},[127],[60,5744],{"className":5745},[131,132],[60,5747,5749],{"className":5748},[79],[60,5750,5752,5803],{"className":5751},[139,140],[60,5753,5755,5800],{"className":5754},[144],[60,5756,5758,5775,5783],{"className":5757,"style":149},[148],[60,5759,5760,5763],{"style":152},[60,5761],{"className":5762,"style":157},[156],[60,5764,5766],{"className":5765},[161,162,163,164],[60,5767,5769,5772],{"className":5768},[127,164],[60,5770,87],{"className":5771,"style":171},[127,164],[60,5773,100],{"className":5774,"style":179},[127,178,164],[60,5776,5777,5780],{"style":225},[60,5778],{"className":5779,"style":157},[156],[60,5781],{"className":5782,"style":233},[232],[60,5784,5785,5788],{"style":236},[60,5786],{"className":5787,"style":157},[156],[60,5789,5791],{"className":5790},[161,162,163,164],[60,5792,5794,5797],{"className":5793},[127,164],[60,5795,87],{"className":5796,"style":171},[127,164],[60,5798,562],{"className":5799,"style":639},[127,178,164],[60,5801,213],{"className":5802},[212],[60,5804,5806],{"className":5805},[144],[60,5807,5809],{"className":5808,"style":261},[148],[60,5810],{},[60,5812],{"className":5813},[267,132],[60,5815,2173],{"className":5816},[127,178],[60,5818,2152],{"className":5819},[127,178],[60,5821,5823],{"className":5822,"style":2331},[267,2330],[60,5824,405],{"className":5825},[2335,2336],"\n将 ",[60,5828,5830,5866],{"className":5829},[63],[60,5831,5833],{"className":5832},[67],[69,5834,5835],{"xmlns":71},[73,5836,5837,5863],{},[76,5838,5839,5853,5855,5857,5859,5861],{},[79,5840,5841,5847],{},[76,5842,5843,5845],{},[84,5844,87],{"mathvariant":86},[84,5846,562],{},[76,5848,5849,5851],{},[84,5850,87],{"mathvariant":86},[84,5852,100],{},[397,5854,448],{},[84,5856,3539],{},[397,5858,400],{"stretchy":399},[84,5860,359],{},[397,5862,405],{"stretchy":399},[106,5864,5865],{"encoding":108},"\\frac{\\partial f}{\\partial y} = P(x)",[60,5867,5869,5958],{"className":5868,"ariaHidden":114},[113],[60,5870,5872,5875,5949,5952,5955],{"className":5871},[118],[60,5873],{"className":5874,"style":123},[122],[60,5876,5878,5881,5946],{"className":5877},[127],[60,5879],{"className":5880},[131,132],[60,5882,5884],{"className":5883},[79],[60,5885,5887,5938],{"className":5886},[139,140],[60,5888,5890,5935],{"className":5889},[144],[60,5891,5893,5910,5918],{"className":5892,"style":149},[148],[60,5894,5895,5898],{"style":152},[60,5896],{"className":5897,"style":157},[156],[60,5899,5901],{"className":5900},[161,162,163,164],[60,5902,5904,5907],{"className":5903},[127,164],[60,5905,87],{"className":5906,"style":171},[127,164],[60,5908,100],{"className":5909,"style":179},[127,178,164],[60,5911,5912,5915],{"style":225},[60,5913],{"className":5914,"style":157},[156],[60,5916],{"className":5917,"style":233},[232],[60,5919,5920,5923],{"style":236},[60,5921],{"className":5922,"style":157},[156],[60,5924,5926],{"className":5925},[161,162,163,164],[60,5927,5929,5932],{"className":5928},[127,164],[60,5930,87],{"className":5931,"style":171},[127,164],[60,5933,562],{"className":5934,"style":639},[127,178,164],[60,5936,213],{"className":5937},[212],[60,5939,5941],{"className":5940},[144],[60,5942,5944],{"className":5943,"style":261},[148],[60,5945],{},[60,5947],{"className":5948},[267,132],[60,5950],{"className":5951,"style":470},[469],[60,5953,448],{"className":5954},[474],[60,5956],{"className":5957,"style":470},[469],[60,5959,5961,5964,5967,5970,5973],{"className":5960},[118],[60,5962],{"className":5963,"style":418},[122],[60,5965,3539],{"className":5966,"style":3572},[127,178],[60,5968,400],{"className":5969},[131],[60,5971,359],{"className":5972},[127,178],[60,5974,405],{"className":5975},[267]," 代入（注意积分变量用 ",[60,5978,5980,5993],{"className":5979},[63],[60,5981,5983],{"className":5982},[67],[69,5984,5985],{"xmlns":71},[73,5986,5987,5991],{},[76,5988,5989],{},[84,5990,2152],{},[106,5992,2152],{"encoding":108},[60,5994,5996],{"className":5995,"ariaHidden":114},[113],[60,5997,5999,6003],{"className":5998},[118],[60,6000],{"className":6001,"style":6002},[122],"height:0.6151em;",[60,6004,2152],{"className":6005},[127,178]," 以示区别）：\n",[60,6008,6010,6077],{"className":6009},[63],[60,6011,6013],{"className":6012},[67],[69,6014,6015],{"xmlns":71},[73,6016,6017,6074],{},[76,6018,6019,6038,6040,6042,6044],{},[79,6020,6021,6028],{},[76,6022,6023,6026],{},[84,6024,87],{"mathvariant":6025},"bold",[84,6027,90],{"mathvariant":6025},[76,6029,6030,6032],{},[84,6031,87],{"mathvariant":6025},[96,6033,6034,6036],{},[84,6035,100],{"mathvariant":6025},[102,6037,104],{"mathvariant":6025},[397,6039,448],{},[84,6041,2119],{},[397,6043,1465],{},[76,6045,6046,6048,6060,6062,6064,6066,6068,6070,6072],{},[397,6047,400],{"fence":114},[2127,6049,6050,6052,6058],{},[397,6051,2131],{},[96,6053,6054,6056],{},[84,6055,359],{"mathvariant":6025},[102,6057,104],{"mathvariant":6025},[84,6059,359],{"mathvariant":6025},[84,6061,3539],{"mathvariant":6025},[397,6063,400],{"stretchy":399},[84,6065,2152],{"mathvariant":6025},[397,6067,405],{"stretchy":399},[84,6069,2173],{"mathvariant":6025},[84,6071,2152],{"mathvariant":6025},[397,6073,405],{"fence":114},[106,6075,6076],{"encoding":108},"\\mathbf{\\frac{\\partial \\varphi}{\\partial y_0} = \\exp\\left( \\int_{x_0}^x P(t) dt \\right)}",[60,6078,6080],{"className":6079,"ariaHidden":114},[113],[60,6081,6083,6086],{"className":6082},[118],[60,6084],{"className":6085,"style":2316},[122],[60,6087,6089,6204,6207,6210,6213,6216,6219],{"className":6088},[127],[60,6090,6092,6095,6201],{"className":6091},[127],[60,6093],{"className":6094},[131,132],[60,6096,6098],{"className":6097},[79],[60,6099,6101,6193],{"className":6100},[139,140],[60,6102,6104,6190],{"className":6103},[144],[60,6105,6107,6165,6173],{"className":6106,"style":149},[148],[60,6108,6109,6112],{"style":152},[60,6110],{"className":6111,"style":157},[156],[60,6113,6115],{"className":6114},[161,162,163,164],[60,6116,6118,6123],{"className":6117},[127,164],[60,6119,87],{"className":6120,"style":6122},[127,6121,164],"mathbf","margin-right:0.0639em;",[60,6124,6126,6130],{"className":6125},[127,164],[60,6127,100],{"className":6128,"style":6129},[127,6121,164],"margin-right:0.016em;",[60,6131,6133],{"className":6132},[183],[60,6134,6136,6157],{"className":6135},[139,140],[60,6137,6139,6154],{"className":6138},[144],[60,6140,6142],{"className":6141,"style":193},[148],[60,6143,6145,6148],{"style":6144},"top:-2.357em;margin-left:-0.016em;margin-right:0.0714em;",[60,6146],{"className":6147,"style":200},[156],[60,6149,6151],{"className":6150},[161,204,205,164],[60,6152,104],{"className":6153},[127,6121,164],[60,6155,213],{"className":6156},[212],[60,6158,6160],{"className":6159},[144],[60,6161,6163],{"className":6162,"style":220},[148],[60,6164],{},[60,6166,6167,6170],{"style":225},[60,6168],{"className":6169,"style":157},[156],[60,6171],{"className":6172,"style":233},[232],[60,6174,6175,6178],{"style":236},[60,6176],{"className":6177,"style":157},[156],[60,6179,6181],{"className":6180},[161,162,163,164],[60,6182,6184,6187],{"className":6183},[127,164],[60,6185,87],{"className":6186,"style":6122},[127,6121,164],[60,6188,90],{"className":6189},[127,178,164],[60,6191,213],{"className":6192},[212],[60,6194,6196],{"className":6195},[144],[60,6197,6199],{"className":6198,"style":261},[148],[60,6200],{},[60,6202],{"className":6203},[267,132],[60,6205],{"className":6206,"style":470},[469],[60,6208,448],{"className":6209},[474],[60,6211],{"className":6212,"style":470},[469],[60,6214,2119],{"className":6215},[1495],[60,6217],{"className":6218,"style":653},[469],[60,6220,6222,6228,6320,6323,6326,6329,6332,6335,6339],{"className":6221},[2326],[60,6223,6225],{"className":6224,"style":2331},[131,2330],[60,6226,400],{"className":6227},[2335,2336],[60,6229,6231,6234],{"className":6230},[1495],[60,6232,2131],{"className":6233,"style":2345},[1495,2343,2344],[60,6235,6237],{"className":6236},[183],[60,6238,6240,6312],{"className":6239},[139,140],[60,6241,6243,6309],{"className":6242},[144],[60,6244,6247,6298],{"className":6245,"style":6246},[148],"height:0.869em;",[60,6248,6249,6252],{"style":2361},[60,6250],{"className":6251,"style":325},[156],[60,6253,6255],{"className":6254},[161,162,163,164],[60,6256,6258],{"className":6257},[127,164],[60,6259,6261,6264],{"className":6260},[127,164],[60,6262,359],{"className":6263},[127,6121,164],[60,6265,6267],{"className":6266},[183],[60,6268,6270,6290],{"className":6269},[139,140],[60,6271,6273,6287],{"className":6272},[144],[60,6274,6276],{"className":6275,"style":193},[148],[60,6277,6278,6281],{"style":2391},[60,6279],{"className":6280,"style":200},[156],[60,6282,6284],{"className":6283},[161,204,205,164],[60,6285,104],{"className":6286},[127,6121,164],[60,6288,213],{"className":6289},[212],[60,6291,6293],{"className":6292},[144],[60,6294,6296],{"className":6295,"style":220},[148],[60,6297],{},[60,6299,6300,6303],{"style":2414},[60,6301],{"className":6302,"style":325},[156],[60,6304,6306],{"className":6305},[161,162,163,164],[60,6307,359],{"className":6308},[127,6121,164],[60,6310,213],{"className":6311},[212],[60,6313,6315],{"className":6314},[144],[60,6316,6318],{"className":6317,"style":2433},[148],[60,6319],{},[60,6321],{"className":6322,"style":653},[469],[60,6324,3539],{"className":6325},[127,6121],[60,6327,400],{"className":6328},[131],[60,6330,2152],{"className":6331},[127,6121],[60,6333,405],{"className":6334},[267],[60,6336,6338],{"className":6337},[127,6121],"dt",[60,6340,6342],{"className":6341,"style":2331},[267,2330],[60,6343,405],{"className":6344},[2335,2336],[6346,6347,6348,6349,6377,6378,6406,6407,6451],"em",{},"(解释：这就是如果你的初始 ",[60,6350,6352,6365],{"className":6351},[63],[60,6353,6355],{"className":6354},[67],[69,6356,6357],{"xmlns":71},[73,6358,6359,6363],{},[76,6360,6361],{},[84,6362,100],{},[106,6364,100],{"encoding":108},[60,6366,6368],{"className":6367,"ariaHidden":114},[113],[60,6369,6371,6374],{"className":6370},[118],[60,6372],{"className":6373,"style":299},[122],[60,6375,100],{"className":6376,"style":179},[127,178]," 值改变一点点，解在 ",[60,6379,6381,6394],{"className":6380},[63],[60,6382,6384],{"className":6383},[67],[69,6385,6386],{"xmlns":71},[73,6387,6388,6392],{},[76,6389,6390],{},[84,6391,359],{},[106,6393,359],{"encoding":108},[60,6395,6397],{"className":6396,"ariaHidden":114},[113],[60,6398,6400,6403],{"className":6399},[118],[60,6401],{"className":6402,"style":371},[122],[60,6404,359],{"className":6405},[127,178]," 处变化的大小。因为它是一阶线性方程，这个放大因子只与 ",[60,6408,6410,6430],{"className":6409},[63],[60,6411,6413],{"className":6412},[67],[69,6414,6415],{"xmlns":71},[73,6416,6417,6427],{},[76,6418,6419,6421,6423,6425],{},[84,6420,3539],{},[397,6422,400],{"stretchy":399},[84,6424,359],{},[397,6426,405],{"stretchy":399},[106,6428,6429],{"encoding":108},"P(x)",[60,6431,6433],{"className":6432,"ariaHidden":114},[113],[60,6434,6436,6439,6442,6445,6448],{"className":6435},[118],[60,6437],{"className":6438,"style":418},[122],[60,6440,3539],{"className":6441,"style":3572},[127,178],[60,6443,400],{"className":6444},[131],[60,6446,359],{"className":6447},[127,178],[60,6449,405],{"className":6450},[267]," 有关。)",[23,6453,6454,5420,6611,7153,7154,7293,7294,7417,7418,7474,7475,7816,7817],{},[26,6455,6456,6457,6610],{},"Step 3: 计算 ",[60,6458,6460,6490],{"className":6459},[63],[60,6461,6463],{"className":6462},[67],[69,6464,6465],{"xmlns":71},[73,6466,6467,6487],{},[76,6468,6469],{},[79,6470,6471,6477],{},[76,6472,6473,6475],{},[84,6474,87],{"mathvariant":86},[84,6476,90],{},[76,6478,6479,6481],{},[84,6480,87],{"mathvariant":86},[96,6482,6483,6485],{},[84,6484,359],{},[102,6486,104],{},[106,6488,6489],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial x_0}",[60,6491,6493],{"className":6492,"ariaHidden":114},[113],[60,6494,6496,6499],{"className":6495},[118],[60,6497],{"className":6498,"style":2862},[122],[60,6500,6502,6505,6607],{"className":6501},[127],[60,6503],{"className":6504},[131,132],[60,6506,6508],{"className":6507},[79],[60,6509,6511,6599],{"className":6510},[139,140],[60,6512,6514,6596],{"className":6513},[144],[60,6515,6517,6571,6579],{"className":6516,"style":149},[148],[60,6518,6519,6522],{"style":152},[60,6520],{"className":6521,"style":157},[156],[60,6523,6525],{"className":6524},[161,162,163,164],[60,6526,6528,6531],{"className":6527},[127,164],[60,6529,87],{"className":6530,"style":171},[127,164],[60,6532,6534,6537],{"className":6533},[127,164],[60,6535,359],{"className":6536},[127,178,164],[60,6538,6540],{"className":6539},[183],[60,6541,6543,6563],{"className":6542},[139,140],[60,6544,6546,6560],{"className":6545},[144],[60,6547,6549],{"className":6548,"style":193},[148],[60,6550,6551,6554],{"style":2391},[60,6552],{"className":6553,"style":200},[156],[60,6555,6557],{"className":6556},[161,204,205,164],[60,6558,104],{"className":6559},[127,164],[60,6561,213],{"className":6562},[212],[60,6564,6566],{"className":6565},[144],[60,6567,6569],{"className":6568,"style":220},[148],[60,6570],{},[60,6572,6573,6576],{"style":225},[60,6574],{"className":6575,"style":157},[156],[60,6577],{"className":6578,"style":233},[232],[60,6580,6581,6584],{"style":236},[60,6582],{"className":6583,"style":157},[156],[60,6585,6587],{"className":6586},[161,162,163,164],[60,6588,6590,6593],{"className":6589},[127,164],[60,6591,87],{"className":6592,"style":171},[127,164],[60,6594,90],{"className":6595},[127,178,164],[60,6597,213],{"className":6598},[212],[60,6600,6602],{"className":6601},[144],[60,6603,6605],{"className":6604,"style":2969},[148],[60,6606],{},[60,6608],{"className":6609},[267,132]," (利用公式 3.17)",[60,6612,6614,6710],{"className":6613},[63],[60,6615,6617],{"className":6616},[67],[69,6618,6619],{"xmlns":71},[73,6620,6621,6707],{},[76,6622,6623,6641,6643,6645,6647,6649,6655,6657,6663,6665,6667,6669,6671],{},[79,6624,6625,6631],{},[76,6626,6627,6629],{},[84,6628,87],{"mathvariant":86},[84,6630,90],{},[76,6632,6633,6635],{},[84,6634,87],{"mathvariant":86},[96,6636,6637,6639],{},[84,6638,359],{},[102,6640,104],{},[397,6642,448],{},[397,6644,817],{},[84,6646,562],{},[397,6648,400],{"stretchy":399},[96,6650,6651,6653],{},[84,6652,359],{},[102,6654,104],{},[397,6656,569],{"separator":114},[96,6658,6659,6661],{},[84,6660,100],{},[102,6662,104],{},[397,6664,405],{"stretchy":399},[397,6666,2831],{},[84,6668,2119],{},[397,6670,1465],{},[76,6672,6673,6675,6687,6701,6703,6705],{},[397,6674,400],{"fence":114},[2127,6676,6677,6679,6685],{},[397,6678,2131],{},[96,6680,6681,6683],{},[84,6682,359],{},[102,6684,104],{},[84,6686,359],{},[79,6688,6689,6695],{},[76,6690,6691,6693],{},[84,6692,87],{"mathvariant":86},[84,6694,562],{},[76,6696,6697,6699],{},[84,6698,87],{"mathvariant":86},[84,6700,100],{},[84,6702,2173],{},[84,6704,2152],{},[397,6706,405],{"fence":114},[106,6708,6709],{"encoding":108},"\\frac{\\partial \\varphi}{\\partial x_0} = -f(x_0,y_0) \\cdot \\exp\\left( \\int_{x_0}^x \\frac{\\partial f}{\\partial y} dt \\right)",[60,6711,6713,6839,6952],{"className":6712,"ariaHidden":114},[113],[60,6714,6716,6719,6830,6833,6836],{"className":6715},[118],[60,6717],{"className":6718,"style":2862},[122],[60,6720,6722,6725,6827],{"className":6721},[127],[60,6723],{"className":6724},[131,132],[60,6726,6728],{"className":6727},[79],[60,6729,6731,6819],{"className":6730},[139,140],[60,6732,6734,6816],{"className":6733},[144],[60,6735,6737,6791,6799],{"className":6736,"style":149},[148],[60,6738,6739,6742],{"style":152},[60,6740],{"className":6741,"style":157},[156],[60,6743,6745],{"className":6744},[161,162,163,164],[60,6746,6748,6751],{"className":6747},[127,164],[60,6749,87],{"className":6750,"style":171},[127,164],[60,6752,6754,6757],{"className":6753},[127,164],[60,6755,359],{"className":6756},[127,178,164],[60,6758,6760],{"className":6759},[183],[60,6761,6763,6783],{"className":6762},[139,140],[60,6764,6766,6780],{"className":6765},[144],[60,6767,6769],{"className":6768,"style":193},[148],[60,6770,6771,6774],{"style":2391},[60,6772],{"className":6773,"style":200},[156],[60,6775,6777],{"className":6776},[161,204,205,164],[60,6778,104],{"className":6779},[127,164],[60,6781,213],{"className":6782},[212],[60,6784,6786],{"className":6785},[144],[60,6787,6789],{"className":6788,"style":220},[148],[60,6790],{},[60,6792,6793,6796],{"style":225},[60,6794],{"className":6795,"style":157},[156],[60,6797],{"className":6798,"style":233},[232],[60,6800,6801,6804],{"style":236},[60,6802],{"className":6803,"style":157},[156],[60,6805,6807],{"className":6806},[161,162,163,164],[60,6808,6810,6813],{"className":6809},[127,164],[60,6811,87],{"className":6812,"style":171},[127,164],[60,6814,90],{"className":6815},[127,178,164],[60,6817,213],{"className":6818},[212],[60,6820,6822],{"className":6821},[144],[60,6823,6825],{"className":6824,"style":2969},[148],[60,6826],{},[60,6828],{"className":6829},[267,132],[60,6831],{"className":6832,"style":470},[469],[60,6834,448],{"className":6835},[474],[60,6837],{"className":6838,"style":470},[469],[60,6840,6842,6845,6848,6851,6854,6894,6897,6900,6940,6943,6946,6949],{"className":6841},[118],[60,6843],{"className":6844,"style":418},[122],[60,6846,817],{"className":6847},[127],[60,6849,562],{"className":6850,"style":639},[127,178],[60,6852,400],{"className":6853},[131],[60,6855,6857,6860],{"className":6856},[127],[60,6858,359],{"className":6859},[127,178],[60,6861,6863],{"className":6862},[183],[60,6864,6866,6886],{"className":6865},[139,140],[60,6867,6869,6883],{"className":6868},[144],[60,6870,6872],{"className":6871,"style":318},[148],[60,6873,6874,6877],{"style":1940},[60,6875],{"className":6876,"style":325},[156],[60,6878,6880],{"className":6879},[161,162,163,164],[60,6881,104],{"className":6882},[127,164],[60,6884,213],{"className":6885},[212],[60,6887,6889],{"className":6888},[144],[60,6890,6892],{"className":6891,"style":341},[148],[60,6893],{},[60,6895,569],{"className":6896},[649],[60,6898],{"className":6899,"style":653},[469],[60,6901,6903,6906],{"className":6902},[127],[60,6904,100],{"className":6905,"style":179},[127,178],[60,6907,6909],{"className":6908},[183],[60,6910,6912,6932],{"className":6911},[139,140],[60,6913,6915,6929],{"className":6914},[144],[60,6916,6918],{"className":6917,"style":318},[148],[60,6919,6920,6923],{"style":321},[60,6921],{"className":6922,"style":325},[156],[60,6924,6926],{"className":6925},[161,162,163,164],[60,6927,104],{"className":6928},[127,164],[60,6930,213],{"className":6931},[212],[60,6933,6935],{"className":6934},[144],[60,6936,6938],{"className":6937,"style":341},[148],[60,6939],{},[60,6941,405],{"className":6942},[267],[60,6944],{"className":6945,"style":924},[469],[60,6947,2831],{"className":6948},[928],[60,6950],{"className":6951,"style":924},[469],[60,6953,6955,6958,6961,6964],{"className":6954},[118],[60,6956],{"className":6957,"style":2316},[122],[60,6959,2119],{"className":6960},[1495],[60,6962],{"className":6963,"style":653},[469],[60,6965,6967,6973,7064,7067,7141,7144,7147],{"className":6966},[2326],[60,6968,6970],{"className":6969,"style":2331},[131,2330],[60,6971,400],{"className":6972},[2335,2336],[60,6974,6976,6979],{"className":6975},[1495],[60,6977,2131],{"className":6978,"style":2345},[1495,2343,2344],[60,6980,6982],{"className":6981},[183],[60,6983,6985,7056],{"className":6984},[139,140],[60,6986,6988,7053],{"className":6987},[144],[60,6989,6991,7042],{"className":6990,"style":2358},[148],[60,6992,6993,6996],{"style":2361},[60,6994],{"className":6995,"style":325},[156],[60,6997,6999],{"className":6998},[161,162,163,164],[60,7000,7002],{"className":7001},[127,164],[60,7003,7005,7008],{"className":7004},[127,164],[60,7006,359],{"className":7007},[127,178,164],[60,7009,7011],{"className":7010},[183],[60,7012,7014,7034],{"className":7013},[139,140],[60,7015,7017,7031],{"className":7016},[144],[60,7018,7020],{"className":7019,"style":193},[148],[60,7021,7022,7025],{"style":2391},[60,7023],{"className":7024,"style":200},[156],[60,7026,7028],{"className":7027},[161,204,205,164],[60,7029,104],{"className":7030},[127,164],[60,7032,213],{"className":7033},[212],[60,7035,7037],{"className":7036},[144],[60,7038,7040],{"className":7039,"style":220},[148],[60,7041],{},[60,7043,7044,7047],{"style":2414},[60,7045],{"className":7046,"style":325},[156],[60,7048,7050],{"className":7049},[161,162,163,164],[60,7051,359],{"className":7052},[127,178,164],[60,7054,213],{"className":7055},[212],[60,7057,7059],{"className":7058},[144],[60,7060,7062],{"className":7061,"style":2433},[148],[60,7063],{},[60,7065],{"className":7066,"style":653},[469],[60,7068,7070,7073,7138],{"className":7069},[127],[60,7071],{"className":7072},[131,132],[60,7074,7076],{"className":7075},[79],[60,7077,7079,7130],{"className":7078},[139,140],[60,7080,7082,7127],{"className":7081},[144],[60,7083,7085,7102,7110],{"className":7084,"style":149},[148],[60,7086,7087,7090],{"style":152},[60,7088],{"className":7089,"style":157},[156],[60,7091,7093],{"className":7092},[161,162,163,164],[60,7094,7096,7099],{"className":7095},[127,164],[60,7097,87],{"className":7098,"style":171},[127,164],[60,7100,100],{"className":7101,"style":179},[127,178,164],[60,7103,7104,7107],{"style":225},[60,7105],{"className":7106,"style":157},[156],[60,7108],{"className":7109,"style":233},[232],[60,7111,7112,7115],{"style":236},[60,7113],{"className":7114,"style":157},[156],[60,7116,7118],{"className":7117},[161,162,163,164],[60,7119,7121,7124],{"className":7120},[127,164],[60,7122,87],{"className":7123,"style":171},[127,164],[60,7125,562],{"className":7126,"style":639},[127,178,164],[60,7128,213],{"className":7129},[212],[60,7131,7133],{"className":7132},[144],[60,7134,7136],{"className":7135,"style":261},[148],[60,7137],{},[60,7139],{"className":7140},[267,132],[60,7142,2173],{"className":7143},[127,178],[60,7145,2152],{"className":7146},[127,178],[60,7148,7150],{"className":7149,"style":2331},[267,2330],[60,7151,405],{"className":7152},[2335,2336],"\n我们需要先写出 ",[60,7155,7157,7189],{"className":7156},[63],[60,7158,7160],{"className":7159},[67],[69,7161,7162],{"xmlns":71},[73,7163,7164,7186],{},[76,7165,7166,7168,7170,7176,7178,7184],{},[84,7167,562],{},[397,7169,400],{"stretchy":399},[96,7171,7172,7174],{},[84,7173,359],{},[102,7175,104],{},[397,7177,569],{"separator":114},[96,7179,7180,7182],{},[84,7181,100],{},[102,7183,104],{},[397,7185,405],{"stretchy":399},[106,7187,7188],{"encoding":108},"f(x_0, y_0)",[60,7190,7192],{"className":7191,"ariaHidden":114},[113],[60,7193,7195,7198,7201,7204,7244,7247,7250,7290],{"className":7194},[118],[60,7196],{"className":7197,"style":418},[122],[60,7199,562],{"className":7200,"style":639},[127,178],[60,7202,400],{"className":7203},[131],[60,7205,7207,7210],{"className":7206},[127],[60,7208,359],{"className":7209},[127,178],[60,7211,7213],{"className":7212},[183],[60,7214,7216,7236],{"className":7215},[139,140],[60,7217,7219,7233],{"className":7218},[144],[60,7220,7222],{"className":7221,"style":318},[148],[60,7223,7224,7227],{"style":1940},[60,7225],{"className":7226,"style":325},[156],[60,7228,7230],{"className":7229},[161,162,163,164],[60,7231,104],{"className":7232},[127,164],[60,7234,213],{"className":7235},[212],[60,7237,7239],{"className":7238},[144],[60,7240,7242],{"className":7241,"style":341},[148],[60,7243],{},[60,7245,569],{"className":7246},[649],[60,7248],{"className":7249,"style":653},[469],[60,7251,7253,7256],{"className":7252},[127],[60,7254,100],{"className":7255,"style":179},[127,178],[60,7257,7259],{"className":7258},[183],[60,7260,7262,7282],{"className":7261},[139,140],[60,7263,7265,7279],{"className":7264},[144],[60,7266,7268],{"className":7267,"style":318},[148],[60,7269,7270,7273],{"style":321},[60,7271],{"className":7272,"style":325},[156],[60,7274,7276],{"className":7275},[161,162,163,164],[60,7277,104],{"className":7278},[127,164],[60,7280,213],{"className":7281},[212],[60,7283,7285],{"className":7284},[144],[60,7286,7288],{"className":7287,"style":341},[148],[60,7289],{},[60,7291,405],{"className":7292},[267],"。将 ",[60,7295,7297,7322],{"className":7296},[63],[60,7298,7300],{"className":7299},[67],[69,7301,7302],{"xmlns":71},[73,7303,7304,7320],{},[76,7305,7306,7312,7314],{},[96,7307,7308,7310],{},[84,7309,359],{},[102,7311,104],{},[397,7313,569],{"separator":114},[96,7315,7316,7318],{},[84,7317,100],{},[102,7319,104],{},[106,7321,1910],{"encoding":108},[60,7323,7325],{"className":7324,"ariaHidden":114},[113],[60,7326,7328,7331,7371,7374,7377],{"className":7327},[118],[60,7329],{"className":7330,"style":299},[122],[60,7332,7334,7337],{"className":7333},[127],[60,7335,359],{"className":7336},[127,178],[60,7338,7340],{"className":7339},[183],[60,7341,7343,7363],{"className":7342},[139,140],[60,7344,7346,7360],{"className":7345},[144],[60,7347,7349],{"className":7348,"style":318},[148],[60,7350,7351,7354],{"style":1940},[60,7352],{"className":7353,"style":325},[156],[60,7355,7357],{"className":7356},[161,162,163,164],[60,7358,104],{"className":7359},[127,164],[60,7361,213],{"className":7362},[212],[60,7364,7366],{"className":7365},[144],[60,7367,7369],{"className":7368,"style":341},[148],[60,7370],{},[60,7372,569],{"className":7373},[649],[60,7375],{"className":7376,"style":653},[469],[60,7378,7380,7383],{"className":7379},[127],[60,7381,100],{"className":7382,"style":179},[127,178],[60,7384,7386],{"className":7385},[183],[60,7387,7389,7409],{"className":7388},[139,140],[60,7390,7392,7406],{"className":7391},[144],[60,7393,7395],{"className":7394,"style":318},[148],[60,7396,7397,7400],{"style":321},[60,7398],{"className":7399,"style":325},[156],[60,7401,7403],{"className":7402},[161,162,163,164],[60,7404,104],{"className":7405},[127,164],[60,7407,213],{"className":7408},[212],[60,7410,7412],{"className":7411},[144],[60,7413,7415],{"className":7414,"style":341},[148],[60,7416],{}," 代入 ",[60,7419,7421,7444],{"className":7420},[63],[60,7422,7424],{"className":7423},[67],[69,7425,7426],{"xmlns":71},[73,7427,7428,7442],{},[76,7429,7430,7432,7434,7436,7438,7440],{},[84,7431,562],{},[397,7433,400],{"stretchy":399},[84,7435,359],{},[397,7437,569],{"separator":114},[84,7439,100],{},[397,7441,405],{"stretchy":399},[106,7443,4410],{"encoding":108},[60,7445,7447],{"className":7446,"ariaHidden":114},[113],[60,7448,7450,7453,7456,7459,7462,7465,7468,7471],{"className":7449},[118],[60,7451],{"className":7452,"style":418},[122],[60,7454,562],{"className":7455,"style":639},[127,178],[60,7457,400],{"className":7458},[131],[60,7460,359],{"className":7461},[127,178],[60,7463,569],{"className":7464},[649],[60,7466],{"className":7467,"style":653},[469],[60,7469,100],{"className":7470,"style":179},[127,178],[60,7472,405],{"className":7473},[267]," 的表达式：\n",[60,7476,7478,7544],{"className":7477},[63],[60,7479,7481],{"className":7480},[67],[69,7482,7483],{"xmlns":71},[73,7484,7485,7541],{},[76,7486,7487,7489,7491,7497,7499,7505,7507,7509,7511,7513,7519,7521,7527,7529,7531,7533,7539],{},[84,7488,562],{},[397,7490,400],{"stretchy":399},[96,7492,7493,7495],{},[84,7494,359],{},[102,7496,104],{},[397,7498,569],{"separator":114},[96,7500,7501,7503],{},[84,7502,100],{},[102,7504,104],{},[397,7506,405],{"stretchy":399},[397,7508,448],{},[84,7510,3539],{},[397,7512,400],{"stretchy":399},[96,7514,7515,7517],{},[84,7516,359],{},[102,7518,104],{},[397,7520,405],{"stretchy":399},[96,7522,7523,7525],{},[84,7524,100],{},[102,7526,104],{},[397,7528,990],{},[84,7530,3550],{},[397,7532,400],{"stretchy":399},[96,7534,7535,7537],{},[84,7536,359],{},[102,7538,104],{},[397,7540,405],{"stretchy":399},[106,7542,7543],{"encoding":108},"f(x_0, y_0) = P(x_0)y_0 + Q(x_0)",[60,7545,7547,7657,7761],{"className":7546,"ariaHidden":114},[113],[60,7548,7550,7553,7556,7559,7599,7602,7605,7645,7648,7651,7654],{"className":7549},[118],[60,7551],{"className":7552,"style":418},[122],[60,7554,562],{"className":7555,"style":639},[127,178],[60,7557,400],{"className":7558},[131],[60,7560,7562,7565],{"className":7561},[127],[60,7563,359],{"className":7564},[127,178],[60,7566,7568],{"className":7567},[183],[60,7569,7571,7591],{"className":7570},[139,140],[60,7572,7574,7588],{"className":7573},[144],[60,7575,7577],{"className":7576,"style":318},[148],[60,7578,7579,7582],{"style":1940},[60,7580],{"className":7581,"style":325},[156],[60,7583,7585],{"className":7584},[161,162,163,164],[60,7586,104],{"className":7587},[127,164],[60,7589,213],{"className":7590},[212],[60,7592,7594],{"className":7593},[144],[60,7595,7597],{"className":7596,"style":341},[148],[60,7598],{},[60,7600,569],{"className":7601},[649],[60,7603],{"className":7604,"style":653},[469],[60,7606,7608,7611],{"className":7607},[127],[60,7609,100],{"className":7610,"style":179},[127,178],[60,7612,7614],{"className":7613},[183],[60,7615,7617,7637],{"className":7616},[139,140],[60,7618,7620,7634],{"className":7619},[144],[60,7621,7623],{"className":7622,"style":318},[148],[60,7624,7625,7628],{"style":321},[60,7626],{"className":7627,"style":325},[156],[60,7629,7631],{"className":7630},[161,162,163,164],[60,7632,104],{"className":7633},[127,164],[60,7635,213],{"className":7636},[212],[60,7638,7640],{"className":7639},[144],[60,7641,7643],{"className":7642,"style":341},[148],[60,7644],{},[60,7646,405],{"className":7647},[267],[60,7649],{"className":7650,"style":470},[469],[60,7652,448],{"className":7653},[474],[60,7655],{"className":7656,"style":470},[469],[60,7658,7660,7663,7666,7669,7709,7712,7752,7755,7758],{"className":7659},[118],[60,7661],{"className":7662,"style":418},[122],[60,7664,3539],{"className":7665,"style":3572},[127,178],[60,7667,400],{"className":7668},[131],[60,7670,7672,7675],{"className":7671},[127],[60,7673,359],{"className":7674},[127,178],[60,7676,7678],{"className":7677},[183],[60,7679,7681,7701],{"className":7680},[139,140],[60,7682,7684,7698],{"className":7683},[144],[60,7685,7687],{"className":7686,"style":318},[148],[60,7688,7689,7692],{"style":1940},[60,7690],{"className":7691,"style":325},[156],[60,7693,7695],{"className":7694},[161,162,163,164],[60,7696,104],{"className":7697},[127,164],[60,7699,213],{"className":7700},[212],[60,7702,7704],{"className":7703},[144],[60,7705,7707],{"className":7706,"style":341},[148],[60,7708],{},[60,7710,405],{"className":7711},[267],[60,7713,7715,7718],{"className":7714},[127],[60,7716,100],{"className":7717,"style":179},[127,178],[60,7719,7721],{"className":7720},[183],[60,7722,7724,7744],{"className":7723},[139,140],[60,7725,7727,7741],{"className":7726},[144],[60,7728,7730],{"className":7729,"style":318},[148],[60,7731,7732,7735],{"style":321},[60,7733],{"className":7734,"style":325},[156],[60,7736,7738],{"className":7737},[161,162,163,164],[60,7739,104],{"className":7740},[127,164],[60,7742,213],{"className":7743},[212],[60,7745,7747],{"className":7746},[144],[60,7748,7750],{"className":7749,"style":341},[148],[60,7751],{},[60,7753],{"className":7754,"style":924},[469],[60,7756,990],{"className":7757},[928],[60,7759],{"className":7760,"style":924},[469],[60,7762,7764,7767,7770,7773,7813],{"className":7763},[118],[60,7765],{"className":7766,"style":418},[122],[60,7768,3550],{"className":7769},[127,178],[60,7771,400],{"className":7772},[131],[60,7774,7776,7779],{"className":7775},[127],[60,7777,359],{"className":7778},[127,178],[60,7780,7782],{"className":7781},[183],[60,7783,7785,7805],{"className":7784},[139,140],[60,7786,7788,7802],{"className":7787},[144],[60,7789,7791],{"className":7790,"style":318},[148],[60,7792,7793,7796],{"style":1940},[60,7794],{"className":7795,"style":325},[156],[60,7797,7799],{"className":7798},[161,162,163,164],[60,7800,104],{"className":7801},[127,164],[60,7803,213],{"className":7804},[212],[60,7806,7808],{"className":7807},[144],[60,7809,7811],{"className":7810,"style":341},[148],[60,7812],{},[60,7814,405],{"className":7815},[267],"\n结合 Step 2 的结果，得到：\n",[60,7818,7820,7926],{"className":7819},[63],[60,7821,7823],{"className":7822},[67],[69,7824,7825],{"xmlns":71},[73,7826,7827,7923],{},[76,7828,7829,7847,7849,7851,7853,7855,7857,7863,7865,7871,7873,7875,7877,7883,7885,7887,7889,7891,7893],{},[79,7830,7831,7837],{},[76,7832,7833,7835],{},[84,7834,87],{"mathvariant":6025},[84,7836,90],{"mathvariant":6025},[76,7838,7839,7841],{},[84,7840,87],{"mathvariant":6025},[96,7842,7843,7845],{},[84,7844,359],{"mathvariant":6025},[102,7846,104],{"mathvariant":6025},[397,7848,448],{},[397,7850,817],{},[397,7852,4981],{"stretchy":399},[84,7854,3539],{"mathvariant":6025},[397,7856,400],{"stretchy":399},[96,7858,7859,7861],{},[84,7860,359],{"mathvariant":6025},[102,7862,104],{"mathvariant":6025},[397,7864,405],{"stretchy":399},[96,7866,7867,7869],{},[84,7868,100],{"mathvariant":6025},[102,7870,104],{"mathvariant":6025},[397,7872,990],{},[84,7874,3550],{"mathvariant":6025},[397,7876,400],{"stretchy":399},[96,7878,7879,7881],{},[84,7880,359],{"mathvariant":6025},[102,7882,104],{"mathvariant":6025},[397,7884,405],{"stretchy":399},[397,7886,5004],{"stretchy":399},[397,7888,2831],{},[84,7890,2119],{},[397,7892,1465],{},[76,7894,7895,7897,7909,7911,7913,7915,7917,7919,7921],{},[397,7896,400],{"fence":114},[2127,7898,7899,7901,7907],{},[397,7900,2131],{},[96,7902,7903,7905],{},[84,7904,359],{"mathvariant":6025},[102,7906,104],{"mathvariant":6025},[84,7908,359],{"mathvariant":6025},[84,7910,3539],{"mathvariant":6025},[397,7912,400],{"stretchy":399},[84,7914,2152],{"mathvariant":6025},[397,7916,405],{"stretchy":399},[84,7918,2173],{"mathvariant":6025},[84,7920,2152],{"mathvariant":6025},[397,7922,405],{"fence":114},[106,7924,7925],{"encoding":108},"\\mathbf{\\frac{\\partial \\varphi}{\\partial x_0} = -[P(x_0)y_0 + Q(x_0)] \\cdot \\exp\\left( \\int_{x_0}^x P(t) dt \\right)}",[60,7927,7929],{"className":7928,"ariaHidden":114},[113],[60,7930,7932,7935],{"className":7931},[118],[60,7933],{"className":7934,"style":2316},[122],[60,7936,7938,8049,8052,8055,8058,8061,8064,8067,8070,8110,8113,8154,8157,8160,8163,8166,8169,8209,8212,8215,8218,8221,8224,8227],{"className":7937},[127],[60,7939,7941,7944,8046],{"className":7940},[127],[60,7942],{"className":7943},[131,132],[60,7945,7947],{"className":7946},[79],[60,7948,7950,8038],{"className":7949},[139,140],[60,7951,7953,8035],{"className":7952},[144],[60,7954,7956,8010,8018],{"className":7955,"style":149},[148],[60,7957,7958,7961],{"style":152},[60,7959],{"className":7960,"style":157},[156],[60,7962,7964],{"className":7963},[161,162,163,164],[60,7965,7967,7970],{"className":7966},[127,164],[60,7968,87],{"className":7969,"style":6122},[127,6121,164],[60,7971,7973,7976],{"className":7972},[127,164],[60,7974,359],{"className":7975},[127,6121,164],[60,7977,7979],{"className":7978},[183],[60,7980,7982,8002],{"className":7981},[139,140],[60,7983,7985,7999],{"className":7984},[144],[60,7986,7988],{"className":7987,"style":193},[148],[60,7989,7990,7993],{"style":2391},[60,7991],{"className":7992,"style":200},[156],[60,7994,7996],{"className":7995},[161,204,205,164],[60,7997,104],{"className":7998},[127,6121,164],[60,8000,213],{"className":8001},[212],[60,8003,8005],{"className":8004},[144],[60,8006,8008],{"className":8007,"style":220},[148],[60,8009],{},[60,8011,8012,8015],{"style":225},[60,8013],{"className":8014,"style":157},[156],[60,8016],{"className":8017,"style":233},[232],[60,8019,8020,8023],{"style":236},[60,8021],{"className":8022,"style":157},[156],[60,8024,8026],{"className":8025},[161,162,163,164],[60,8027,8029,8032],{"className":8028},[127,164],[60,8030,87],{"className":8031,"style":6122},[127,6121,164],[60,8033,90],{"className":8034},[127,178,164],[60,8036,213],{"className":8037},[212],[60,8039,8041],{"className":8040},[144],[60,8042,8044],{"className":8043,"style":2969},[148],[60,8045],{},[60,8047],{"className":8048},[267,132],[60,8050],{"className":8051,"style":470},[469],[60,8053,448],{"className":8054},[474],[60,8056],{"className":8057,"style":470},[469],[60,8059,817],{"className":8060},[127],[60,8062,4981],{"className":8063},[131],[60,8065,3539],{"className":8066},[127,6121],[60,8068,400],{"className":8069},[131],[60,8071,8073,8076],{"className":8072},[127],[60,8074,359],{"className":8075},[127,6121],[60,8077,8079],{"className":8078},[183],[60,8080,8082,8102],{"className":8081},[139,140],[60,8083,8085,8099],{"className":8084},[144],[60,8086,8088],{"className":8087,"style":318},[148],[60,8089,8090,8093],{"style":1940},[60,8091],{"className":8092,"style":325},[156],[60,8094,8096],{"className":8095},[161,162,163,164],[60,8097,104],{"className":8098},[127,6121,164],[60,8100,213],{"className":8101},[212],[60,8103,8105],{"className":8104},[144],[60,8106,8108],{"className":8107,"style":341},[148],[60,8109],{},[60,8111,405],{"className":8112},[267],[60,8114,8116,8119],{"className":8115},[127],[60,8117,100],{"className":8118,"style":6129},[127,6121],[60,8120,8122],{"className":8121},[183],[60,8123,8125,8146],{"className":8124},[139,140],[60,8126,8128,8143],{"className":8127},[144],[60,8129,8131],{"className":8130,"style":318},[148],[60,8132,8134,8137],{"style":8133},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[60,8135],{"className":8136,"style":325},[156],[60,8138,8140],{"className":8139},[161,162,163,164],[60,8141,104],{"className":8142},[127,6121,164],[60,8144,213],{"className":8145},[212],[60,8147,8149],{"className":8148},[144],[60,8150,8152],{"className":8151,"style":341},[148],[60,8153],{},[60,8155],{"className":8156,"style":924},[469],[60,8158,990],{"className":8159},[928],[60,8161],{"className":8162,"style":924},[469],[60,8164,3550],{"className":8165},[127,6121],[60,8167,400],{"className":8168},[131],[60,8170,8172,8175],{"className":8171},[127],[60,8173,359],{"className":8174},[127,6121],[60,8176,8178],{"className":8177},[183],[60,8179,8181,8201],{"className":8180},[139,140],[60,8182,8184,8198],{"className":8183},[144],[60,8185,8187],{"className":8186,"style":318},[148],[60,8188,8189,8192],{"style":1940},[60,8190],{"className":8191,"style":325},[156],[60,8193,8195],{"className":8194},[161,162,163,164],[60,8196,104],{"className":8197},[127,6121,164],[60,8199,213],{"className":8200},[212],[60,8202,8204],{"className":8203},[144],[60,8205,8207],{"className":8206,"style":341},[148],[60,8208],{},[60,8210,5234],{"className":8211},[267],[60,8213],{"className":8214,"style":924},[469],[60,8216,2831],{"className":8217},[928],[60,8219],{"className":8220,"style":924},[469],[60,8222,2119],{"className":8223},[1495],[60,8225],{"className":8226,"style":653},[469],[60,8228,8230,8236,8327,8330,8333,8336,8339,8342,8345],{"className":8229},[2326],[60,8231,8233],{"className":8232,"style":2331},[131,2330],[60,8234,400],{"className":8235},[2335,2336],[60,8237,8239,8242],{"className":8238},[1495],[60,8240,2131],{"className":8241,"style":2345},[1495,2343,2344],[60,8243,8245],{"className":8244},[183],[60,8246,8248,8319],{"className":8247},[139,140],[60,8249,8251,8316],{"className":8250},[144],[60,8252,8254,8305],{"className":8253,"style":6246},[148],[60,8255,8256,8259],{"style":2361},[60,8257],{"className":8258,"style":325},[156],[60,8260,8262],{"className":8261},[161,162,163,164],[60,8263,8265],{"className":8264},[127,164],[60,8266,8268,8271],{"className":8267},[127,164],[60,8269,359],{"className":8270},[127,6121,164],[60,8272,8274],{"className":8273},[183],[60,8275,8277,8297],{"className":8276},[139,140],[60,8278,8280,8294],{"className":8279},[144],[60,8281,8283],{"className":8282,"style":193},[148],[60,8284,8285,8288],{"style":2391},[60,8286],{"className":8287,"style":200},[156],[60,8289,8291],{"className":8290},[161,204,205,164],[60,8292,104],{"className":8293},[127,6121,164],[60,8295,213],{"className":8296},[212],[60,8298,8300],{"className":8299},[144],[60,8301,8303],{"className":8302,"style":220},[148],[60,8304],{},[60,8306,8307,8310],{"style":2414},[60,8308],{"className":8309,"style":325},[156],[60,8311,8313],{"className":8312},[161,162,163,164],[60,8314,359],{"className":8315},[127,6121,164],[60,8317,213],{"className":8318},[212],[60,8320,8322],{"className":8321},[144],[60,8323,8325],{"className":8324,"style":2433},[148],[60,8326],{},[60,8328],{"className":8329,"style":653},[469],[60,8331,3539],{"className":8332},[127,6121],[60,8334,400],{"className":8335},[131],[60,8337,2152],{"className":8338},[127,6121],[60,8340,405],{"className":8341},[267],[60,8343,6338],{"className":8344},[127,6121],[60,8346,8348],{"className":8347,"style":2331},[267,2330],[60,8349,405],{"className":8350},[2335,2336],[23,8352,8353,8467,8468,8496,8497,8608,8609,8671,8672],{},[26,8354,8355,8356],{},"Step 4: 计算 ",[60,8357,8359,8384],{"className":8358},[63],[60,8360,8362],{"className":8361},[67],[69,8363,8364],{"xmlns":71},[73,8365,8366,8382],{},[76,8367,8368],{},[79,8369,8370,8376],{},[76,8371,8372,8374],{},[84,8373,87],{"mathvariant":86},[84,8375,90],{},[76,8377,8378,8380],{},[84,8379,87],{"mathvariant":86},[84,8381,359],{},[106,8383,4290],{"encoding":108},[60,8385,8387],{"className":8386,"ariaHidden":114},[113],[60,8388,8390,8393],{"className":8389},[118],[60,8391],{"className":8392,"style":3836},[122],[60,8394,8396,8399,8464],{"className":8395},[127],[60,8397],{"className":8398},[131,132],[60,8400,8402],{"className":8401},[79],[60,8403,8405,8456],{"className":8404},[139,140],[60,8406,8408,8453],{"className":8407},[144],[60,8409,8411,8428,8436],{"className":8410,"style":149},[148],[60,8412,8413,8416],{"style":152},[60,8414],{"className":8415,"style":157},[156],[60,8417,8419],{"className":8418},[161,162,163,164],[60,8420,8422,8425],{"className":8421},[127,164],[60,8423,87],{"className":8424,"style":171},[127,164],[60,8426,359],{"className":8427},[127,178,164],[60,8429,8430,8433],{"style":225},[60,8431],{"className":8432,"style":157},[156],[60,8434],{"className":8435,"style":233},[232],[60,8437,8438,8441],{"style":236},[60,8439],{"className":8440,"style":157},[156],[60,8442,8444],{"className":8443},[161,162,163,164],[60,8445,8447,8450],{"className":8446},[127,164],[60,8448,87],{"className":8449,"style":171},[127,164],[60,8451,90],{"className":8452},[127,178,164],[60,8454,213],{"className":8455},[212],[60,8457,8459],{"className":8458},[144],[60,8460,8462],{"className":8461,"style":3907},[148],[60,8463],{},[60,8465],{"className":8466},[267,132],"\n这个最简单，但容易想复杂。",[60,8469,8471,8484],{"className":8470},[63],[60,8472,8474],{"className":8473},[67],[69,8475,8476],{"xmlns":71},[73,8477,8478,8482],{},[76,8479,8480],{},[84,8481,90],{},[106,8483,1868],{"encoding":108},[60,8485,8487],{"className":8486,"ariaHidden":114},[113],[60,8488,8490,8493],{"className":8489},[118],[60,8491],{"className":8492,"style":299},[122],[60,8494,90],{"className":8495},[127,178]," 是原方程的解。\n解的定义就是：把它代入方程，方程成立。\n即 ",[60,8498,8500,8525],{"className":8499},[63],[60,8501,8503],{"className":8502},[67],[69,8504,8505],{"xmlns":71},[73,8506,8507,8523],{},[76,8508,8509],{},[79,8510,8511,8517],{},[76,8512,8513,8515],{},[84,8514,87],{"mathvariant":86},[84,8516,90],{},[76,8518,8519,8521],{},[84,8520,87],{"mathvariant":86},[84,8522,359],{},[106,8524,4290],{"encoding":108},[60,8526,8528],{"className":8527,"ariaHidden":114},[113],[60,8529,8531,8534],{"className":8530},[118],[60,8532],{"className":8533,"style":3836},[122],[60,8535,8537,8540,8605],{"className":8536},[127],[60,8538],{"className":8539},[131,132],[60,8541,8543],{"className":8542},[79],[60,8544,8546,8597],{"className":8545},[139,140],[60,8547,8549,8594],{"className":8548},[144],[60,8550,8552,8569,8577],{"className":8551,"style":149},[148],[60,8553,8554,8557],{"style":152},[60,8555],{"className":8556,"style":157},[156],[60,8558,8560],{"className":8559},[161,162,163,164],[60,8561,8563,8566],{"className":8562},[127,164],[60,8564,87],{"className":8565,"style":171},[127,164],[60,8567,359],{"className":8568},[127,178,164],[60,8570,8571,8574],{"style":225},[60,8572],{"className":8573,"style":157},[156],[60,8575],{"className":8576,"style":233},[232],[60,8578,8579,8582],{"style":236},[60,8580],{"className":8581,"style":157},[156],[60,8583,8585],{"className":8584},[161,162,163,164],[60,8586,8588,8591],{"className":8587},[127,164],[60,8589,87],{"className":8590,"style":171},[127,164],[60,8592,90],{"className":8593},[127,178,164],[60,8595,213],{"className":8596},[212],[60,8598,8600],{"className":8599},[144],[60,8601,8603],{"className":8602,"style":3907},[148],[60,8604],{},[60,8606],{"className":8607},[267,132]," 就是 ",[60,8610,8612,8630],{"className":8611},[63],[60,8613,8615],{"className":8614},[67],[69,8616,8617],{"xmlns":71},[73,8618,8619,8627],{},[76,8620,8621],{},[550,8622,8623,8625],{},[84,8624,100],{},[397,8626,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,8628,8629],{"encoding":108},"y'",[60,8631,8633],{"className":8632,"ariaHidden":114},[113],[60,8634,8636,8639],{"className":8635},[118],[60,8637],{"className":8638,"style":586},[122],[60,8640,8642,8645],{"className":8641},[127],[60,8643,100],{"className":8644,"style":179},[127,178],[60,8646,8648],{"className":8647},[183],[60,8649,8651],{"className":8650},[139],[60,8652,8654],{"className":8653},[144],[60,8655,8657],{"className":8656,"style":605},[148],[60,8658,8659,8662],{"style":608},[60,8660],{"className":8661,"style":325},[156],[60,8663,8665],{"className":8664},[161,162,163,164],[60,8666,8668],{"className":8667},[127,164],[60,8669,557],{"className":8670},[127,164],"，也就是方程的右端：\n",[60,8673,8675,8759],{"className":8674},[63],[60,8676,8678],{"className":8677},[67],[69,8679,8680],{"xmlns":71},[73,8681,8682,8756],{},[76,8683,8684,8698,8700,8702,8704,8706,8708,8710,8712,8714,8716,8718,8720,8722,8724,8726,8728,8730,8736,8738,8744,8746,8748,8750,8752,8754],{},[79,8685,8686,8692],{},[76,8687,8688,8690],{},[84,8689,87],{"mathvariant":6025},[84,8691,90],{"mathvariant":6025},[76,8693,8694,8696],{},[84,8695,87],{"mathvariant":6025},[84,8697,359],{"mathvariant":6025},[397,8699,448],{},[84,8701,562],{"mathvariant":6025},[397,8703,400],{"stretchy":399},[84,8705,359],{"mathvariant":6025},[397,8707,569],{"separator":114},[84,8709,90],{"mathvariant":6025},[397,8711,405],{"stretchy":399},[397,8713,448],{},[84,8715,3539],{"mathvariant":6025},[397,8717,400],{"stretchy":399},[84,8719,359],{"mathvariant":6025},[397,8721,405],{"stretchy":399},[84,8723,90],{"mathvariant":6025},[397,8725,400],{"stretchy":399},[84,8727,359],{"mathvariant":6025},[397,8729,569],{"separator":114},[96,8731,8732,8734],{},[84,8733,359],{"mathvariant":6025},[102,8735,104],{"mathvariant":6025},[397,8737,569],{"separator":114},[96,8739,8740,8742],{},[84,8741,100],{"mathvariant":6025},[102,8743,104],{"mathvariant":6025},[397,8745,405],{"stretchy":399},[397,8747,990],{},[84,8749,3550],{"mathvariant":6025},[397,8751,400],{"stretchy":399},[84,8753,359],{"mathvariant":6025},[397,8755,405],{"stretchy":399},[106,8757,8758],{"encoding":108},"\\mathbf{\\frac{\\partial \\varphi}{\\partial x} = f(x, \\varphi) = P(x)\\varphi(x,x_0,y_0) + Q(x)}",[60,8760,8762],{"className":8761,"ariaHidden":114},[113],[60,8763,8765,8768],{"className":8764},[118],[60,8766],{"className":8767,"style":3836},[122],[60,8769,8771,8843,8846,8849,8852,8856,8859,8862,8865,8868,8871,8874,8877,8880,8883,8886,8889,8892,8895,8898,8901,8904,8907,8910,8950,8953,8956,8996,8999,9002,9005,9008,9011,9014,9017],{"className":8770},[127],[60,8772,8774,8777,8840],{"className":8773},[127],[60,8775],{"className":8776},[131,132],[60,8778,8780],{"className":8779},[79],[60,8781,8783,8832],{"className":8782},[139,140],[60,8784,8786,8829],{"className":8785},[144],[60,8787,8789,8804,8812],{"className":8788,"style":149},[148],[60,8790,8791,8794],{"style":152},[60,8792],{"className":8793,"style":157},[156],[60,8795,8797],{"className":8796},[161,162,163,164],[60,8798,8800],{"className":8799},[127,164],[60,8801,8803],{"className":8802},[127,6121,164],"∂x",[60,8805,8806,8809],{"style":225},[60,8807],{"className":8808,"style":157},[156],[60,8810],{"className":8811,"style":233},[232],[60,8813,8814,8817],{"style":236},[60,8815],{"className":8816,"style":157},[156],[60,8818,8820],{"className":8819},[161,162,163,164],[60,8821,8823,8826],{"className":8822},[127,164],[60,8824,87],{"className":8825,"style":6122},[127,6121,164],[60,8827,90],{"className":8828},[127,178,164],[60,8830,213],{"className":8831},[212],[60,8833,8835],{"className":8834},[144],[60,8836,8838],{"className":8837,"style":3907},[148],[60,8839],{},[60,8841],{"className":8842},[267,132],[60,8844],{"className":8845,"style":470},[469],[60,8847,448],{"className":8848},[474],[60,8850],{"className":8851,"style":470},[469],[60,8853,562],{"className":8854,"style":8855},[127,6121],"margin-right:0.109em;",[60,8857,400],{"className":8858},[131],[60,8860,359],{"className":8861},[127,6121],[60,8863,569],{"className":8864},[649],[60,8866],{"className":8867,"style":653},[469],[60,8869,90],{"className":8870},[127,178],[60,8872,405],{"className":8873},[267],[60,8875],{"className":8876,"style":470},[469],[60,8878,448],{"className":8879},[474],[60,8881],{"className":8882,"style":470},[469],[60,8884,3539],{"className":8885},[127,6121],[60,8887,400],{"className":8888},[131],[60,8890,359],{"className":8891},[127,6121],[60,8893,405],{"className":8894},[267],[60,8896,90],{"className":8897},[127,178],[60,8899,400],{"className":8900},[131],[60,8902,359],{"className":8903},[127,6121],[60,8905,569],{"className":8906},[649],[60,8908],{"className":8909,"style":653},[469],[60,8911,8913,8916],{"className":8912},[127],[60,8914,359],{"className":8915},[127,6121],[60,8917,8919],{"className":8918},[183],[60,8920,8922,8942],{"className":8921},[139,140],[60,8923,8925,8939],{"className":8924},[144],[60,8926,8928],{"className":8927,"style":318},[148],[60,8929,8930,8933],{"style":1940},[60,8931],{"className":8932,"style":325},[156],[60,8934,8936],{"className":8935},[161,162,163,164],[60,8937,104],{"className":8938},[127,6121,164],[60,8940,213],{"className":8941},[212],[60,8943,8945],{"className":8944},[144],[60,8946,8948],{"className":8947,"style":341},[148],[60,8949],{},[60,8951,569],{"className":8952},[649],[60,8954],{"className":8955,"style":653},[469],[60,8957,8959,8962],{"className":8958},[127],[60,8960,100],{"className":8961,"style":6129},[127,6121],[60,8963,8965],{"className":8964},[183],[60,8966,8968,8988],{"className":8967},[139,140],[60,8969,8971,8985],{"className":8970},[144],[60,8972,8974],{"className":8973,"style":318},[148],[60,8975,8976,8979],{"style":8133},[60,8977],{"className":8978,"style":325},[156],[60,8980,8982],{"className":8981},[161,162,163,164],[60,8983,104],{"className":8984},[127,6121,164],[60,8986,213],{"className":8987},[212],[60,8989,8991],{"className":8990},[144],[60,8992,8994],{"className":8993,"style":341},[148],[60,8995],{},[60,8997,405],{"className":8998},[267],[60,9000],{"className":9001,"style":924},[469],[60,9003,990],{"className":9004},[928],[60,9006],{"className":9007,"style":924},[469],[60,9009,3550],{"className":9010},[127,6121],[60,9012,400],{"className":9013},[131],[60,9015,359],{"className":9016},[127,6121],[60,9018,405],{"className":9019},[267],[15,9021],{},[496,9023,9025],{"id":9024},"题目-2","题目 2",[23,9027,9028,9030,9031,9247,9248,9401,9402,9555,9556,9725],{},[26,9029,3523],{}," 给定方程 ",[60,9032,9034,9073],{"className":9033},[63],[60,9035,9037],{"className":9036},[67],[69,9038,9039],{"xmlns":71},[73,9040,9041,9070],{},[76,9042,9043,9057,9059,9062,9064],{},[79,9044,9045,9051],{},[76,9046,9047,9049],{},[84,9048,2173],{"mathvariant":86},[84,9050,100],{},[76,9052,9053,9055],{},[84,9054,2173],{"mathvariant":86},[84,9056,359],{},[397,9058,448],{},[84,9060,9061],{},"sin",[397,9063,1465],{},[79,9065,9066,9068],{},[84,9067,100],{},[84,9069,359],{},[106,9071,9072],{"encoding":108},"\\frac{\\mathrm{d}y}{\\mathrm{d}x} = \\sin \\frac{y}{x}",[60,9074,9076,9165],{"className":9075,"ariaHidden":114},[113],[60,9077,9079,9082,9156,9159,9162],{"className":9078},[118],[60,9080],{"className":9081,"style":3836},[122],[60,9083,9085,9088,9153],{"className":9084},[127],[60,9086],{"className":9087},[131,132],[60,9089,9091],{"className":9090},[79],[60,9092,9094,9145],{"className":9093},[139,140],[60,9095,9097,9142],{"className":9096},[144],[60,9098,9100,9117,9125],{"className":9099,"style":149},[148],[60,9101,9102,9105],{"style":152},[60,9103],{"className":9104,"style":157},[156],[60,9106,9108],{"className":9107},[161,162,163,164],[60,9109,9111,9114],{"className":9110},[127,164],[60,9112,2173],{"className":9113},[127,3869,164],[60,9115,359],{"className":9116},[127,178,164],[60,9118,9119,9122],{"style":225},[60,9120],{"className":9121,"style":157},[156],[60,9123],{"className":9124,"style":233},[232],[60,9126,9127,9130],{"style":236},[60,9128],{"className":9129,"style":157},[156],[60,9131,9133],{"className":9132},[161,162,163,164],[60,9134,9136,9139],{"className":9135},[127,164],[60,9137,2173],{"className":9138},[127,3869,164],[60,9140,100],{"className":9141,"style":179},[127,178,164],[60,9143,213],{"className":9144},[212],[60,9146,9148],{"className":9147},[144],[60,9149,9151],{"className":9150,"style":3907},[148],[60,9152],{},[60,9154],{"className":9155},[267,132],[60,9157],{"className":9158,"style":470},[469],[60,9160,448],{"className":9161},[474],[60,9163],{"className":9164,"style":470},[469],[60,9166,9168,9172,9175,9178],{"className":9167},[118],[60,9169],{"className":9170,"style":9171},[122],"height:1.0925em;vertical-align:-0.345em;",[60,9173,9061],{"className":9174},[1495],[60,9176],{"className":9177,"style":653},[469],[60,9179,9181,9184,9244],{"className":9180},[127],[60,9182],{"className":9183},[131,132],[60,9185,9187],{"className":9186},[79],[60,9188,9190,9236],{"className":9189},[139,140],[60,9191,9193,9233],{"className":9192},[144],[60,9194,9197,9211,9219],{"className":9195,"style":9196},[148],"height:0.7475em;",[60,9198,9199,9202],{"style":152},[60,9200],{"className":9201,"style":157},[156],[60,9203,9205],{"className":9204},[161,162,163,164],[60,9206,9208],{"className":9207},[127,164],[60,9209,359],{"className":9210},[127,178,164],[60,9212,9213,9216],{"style":225},[60,9214],{"className":9215,"style":157},[156],[60,9217],{"className":9218,"style":233},[232],[60,9220,9221,9224],{"style":236},[60,9222],{"className":9223,"style":157},[156],[60,9225,9227],{"className":9226},[161,162,163,164],[60,9228,9230],{"className":9229},[127,164],[60,9231,100],{"className":9232,"style":179},[127,178,164],[60,9234,213],{"className":9235},[212],[60,9237,9239],{"className":9238},[144],[60,9240,9242],{"className":9241,"style":3907},[148],[60,9243],{},[60,9245],{"className":9246},[267,132],"，求 ",[60,9249,9251,9281],{"className":9250},[63],[60,9252,9254],{"className":9253},[67],[69,9255,9256],{"xmlns":71},[73,9257,9258,9278],{},[76,9259,9260],{},[79,9261,9262,9268],{},[76,9263,9264,9266],{},[84,9265,87],{"mathvariant":86},[84,9267,100],{},[76,9269,9270,9272],{},[84,9271,87],{"mathvariant":86},[96,9273,9274,9276],{},[84,9275,359],{},[102,9277,104],{},[106,9279,9280],{"encoding":108},"\\frac{\\partial y}{\\partial x_0}",[60,9282,9284],{"className":9283,"ariaHidden":114},[113],[60,9285,9287,9290],{"className":9286},[118],[60,9288],{"className":9289,"style":2862},[122],[60,9291,9293,9296,9398],{"className":9292},[127],[60,9294],{"className":9295},[131,132],[60,9297,9299],{"className":9298},[79],[60,9300,9302,9390],{"className":9301},[139,140],[60,9303,9305,9387],{"className":9304},[144],[60,9306,9308,9362,9370],{"className":9307,"style":149},[148],[60,9309,9310,9313],{"style":152},[60,9311],{"className":9312,"style":157},[156],[60,9314,9316],{"className":9315},[161,162,163,164],[60,9317,9319,9322],{"className":9318},[127,164],[60,9320,87],{"className":9321,"style":171},[127,164],[60,9323,9325,9328],{"className":9324},[127,164],[60,9326,359],{"className":9327},[127,178,164],[60,9329,9331],{"className":9330},[183],[60,9332,9334,9354],{"className":9333},[139,140],[60,9335,9337,9351],{"className":9336},[144],[60,9338,9340],{"className":9339,"style":193},[148],[60,9341,9342,9345],{"style":2391},[60,9343],{"className":9344,"style":200},[156],[60,9346,9348],{"className":9347},[161,204,205,164],[60,9349,104],{"className":9350},[127,164],[60,9352,213],{"className":9353},[212],[60,9355,9357],{"className":9356},[144],[60,9358,9360],{"className":9359,"style":220},[148],[60,9361],{},[60,9363,9364,9367],{"style":225},[60,9365],{"className":9366,"style":157},[156],[60,9368],{"className":9369,"style":233},[232],[60,9371,9372,9375],{"style":236},[60,9373],{"className":9374,"style":157},[156],[60,9376,9378],{"className":9377},[161,162,163,164],[60,9379,9381,9384],{"className":9380},[127,164],[60,9382,87],{"className":9383,"style":171},[127,164],[60,9385,100],{"className":9386,"style":179},[127,178,164],[60,9388,213],{"className":9389},[212],[60,9391,9393],{"className":9392},[144],[60,9394,9396],{"className":9395,"style":2969},[148],[60,9397],{},[60,9399],{"className":9400},[267,132]," 和 ",[60,9403,9405,9435],{"className":9404},[63],[60,9406,9408],{"className":9407},[67],[69,9409,9410],{"xmlns":71},[73,9411,9412,9432],{},[76,9413,9414],{},[79,9415,9416,9422],{},[76,9417,9418,9420],{},[84,9419,87],{"mathvariant":86},[84,9421,100],{},[76,9423,9424,9426],{},[84,9425,87],{"mathvariant":86},[96,9427,9428,9430],{},[84,9429,100],{},[102,9431,104],{},[106,9433,9434],{"encoding":108},"\\frac{\\partial y}{\\partial y_0}",[60,9436,9438],{"className":9437,"ariaHidden":114},[113],[60,9439,9441,9444],{"className":9440},[118],[60,9442],{"className":9443,"style":123},[122],[60,9445,9447,9450,9552],{"className":9446},[127],[60,9448],{"className":9449},[131,132],[60,9451,9453],{"className":9452},[79],[60,9454,9456,9544],{"className":9455},[139,140],[60,9457,9459,9541],{"className":9458},[144],[60,9460,9462,9516,9524],{"className":9461,"style":149},[148],[60,9463,9464,9467],{"style":152},[60,9465],{"className":9466,"style":157},[156],[60,9468,9470],{"className":9469},[161,162,163,164],[60,9471,9473,9476],{"className":9472},[127,164],[60,9474,87],{"className":9475,"style":171},[127,164],[60,9477,9479,9482],{"className":9478},[127,164],[60,9480,100],{"className":9481,"style":179},[127,178,164],[60,9483,9485],{"className":9484},[183],[60,9486,9488,9508],{"className":9487},[139,140],[60,9489,9491,9505],{"className":9490},[144],[60,9492,9494],{"className":9493,"style":193},[148],[60,9495,9496,9499],{"style":196},[60,9497],{"className":9498,"style":200},[156],[60,9500,9502],{"className":9501},[161,204,205,164],[60,9503,104],{"className":9504},[127,164],[60,9506,213],{"className":9507},[212],[60,9509,9511],{"className":9510},[144],[60,9512,9514],{"className":9513,"style":220},[148],[60,9515],{},[60,9517,9518,9521],{"style":225},[60,9519],{"className":9520,"style":157},[156],[60,9522],{"className":9523,"style":233},[232],[60,9525,9526,9529],{"style":236},[60,9527],{"className":9528,"style":157},[156],[60,9530,9532],{"className":9531},[161,162,163,164],[60,9533,9535,9538],{"className":9534},[127,164],[60,9536,87],{"className":9537,"style":171},[127,164],[60,9539,100],{"className":9540,"style":179},[127,178,164],[60,9542,213],{"className":9543},[212],[60,9545,9547],{"className":9546},[144],[60,9548,9550],{"className":9549,"style":261},[148],[60,9551],{},[60,9553],{"className":9554},[267,132]," 在 ",[60,9557,9559,9593],{"className":9558},[63],[60,9560,9562],{"className":9561},[67],[69,9563,9564],{"xmlns":71},[73,9565,9566,9590],{},[76,9567,9568,9574,9576,9578,9580,9586,9588],{},[96,9569,9570,9572],{},[84,9571,359],{},[102,9573,104],{},[397,9575,448],{},[102,9577,820],{},[397,9579,569],{"separator":114},[96,9581,9582,9584],{},[84,9583,100],{},[102,9585,104],{},[397,9587,448],{},[102,9589,104],{},[106,9591,9592],{"encoding":108},"x_0 = 1, y_0 = 0",[60,9594,9596,9651,9716],{"className":9595,"ariaHidden":114},[113],[60,9597,9599,9602,9642,9645,9648],{"className":9598},[118],[60,9600],{"className":9601,"style":2734},[122],[60,9603,9605,9608],{"className":9604},[127],[60,9606,359],{"className":9607},[127,178],[60,9609,9611],{"className":9610},[183],[60,9612,9614,9634],{"className":9613},[139,140],[60,9615,9617,9631],{"className":9616},[144],[60,9618,9620],{"className":9619,"style":318},[148],[60,9621,9622,9625],{"style":1940},[60,9623],{"className":9624,"style":325},[156],[60,9626,9628],{"className":9627},[161,162,163,164],[60,9629,104],{"className":9630},[127,164],[60,9632,213],{"className":9633},[212],[60,9635,9637],{"className":9636},[144],[60,9638,9640],{"className":9639,"style":341},[148],[60,9641],{},[60,9643],{"className":9644,"style":470},[469],[60,9646,448],{"className":9647},[474],[60,9649],{"className":9650,"style":470},[469],[60,9652,9654,9658,9661,9664,9667,9707,9710,9713],{"className":9653},[118],[60,9655],{"className":9656,"style":9657},[122],"height:0.8389em;vertical-align:-0.1944em;",[60,9659,820],{"className":9660},[127],[60,9662,569],{"className":9663},[649],[60,9665],{"className":9666,"style":653},[469],[60,9668,9670,9673],{"className":9669},[127],[60,9671,100],{"className":9672,"style":179},[127,178],[60,9674,9676],{"className":9675},[183],[60,9677,9679,9699],{"className":9678},[139,140],[60,9680,9682,9696],{"className":9681},[144],[60,9683,9685],{"className":9684,"style":318},[148],[60,9686,9687,9690],{"style":321},[60,9688],{"className":9689,"style":325},[156],[60,9691,9693],{"className":9692},[161,162,163,164],[60,9694,104],{"className":9695},[127,164],[60,9697,213],{"className":9698},[212],[60,9700,9702],{"className":9701},[144],[60,9703,9705],{"className":9704,"style":341},[148],[60,9706],{},[60,9708],{"className":9709,"style":470},[469],[60,9711,448],{"className":9712},[474],[60,9714],{"className":9715,"style":470},[469],[60,9717,9719,9722],{"className":9718},[118],[60,9720],{"className":9721,"style":484},[122],[60,9723,104],{"className":9724},[127]," 时的表达式。",[23,9727,9728],{},[26,9729,4378],{},[23,9731,9732,9735,9736,9847,9848,9876,9877,9946],{},[26,9733,9734],{},"关键提示："," 对于非线性方程，积分里的 ",[60,9737,9739,9764],{"className":9738},[63],[60,9740,9742],{"className":9741},[67],[69,9743,9744],{"xmlns":71},[73,9745,9746,9762],{},[76,9747,9748],{},[79,9749,9750,9756],{},[76,9751,9752,9754],{},[84,9753,87],{"mathvariant":86},[84,9755,562],{},[76,9757,9758,9760],{},[84,9759,87],{"mathvariant":86},[84,9761,100],{},[106,9763,2585],{"encoding":108},[60,9765,9767],{"className":9766,"ariaHidden":114},[113],[60,9768,9770,9773],{"className":9769},[118],[60,9771],{"className":9772,"style":123},[122],[60,9774,9776,9779,9844],{"className":9775},[127],[60,9777],{"className":9778},[131,132],[60,9780,9782],{"className":9781},[79],[60,9783,9785,9836],{"className":9784},[139,140],[60,9786,9788,9833],{"className":9787},[144],[60,9789,9791,9808,9816],{"className":9790,"style":149},[148],[60,9792,9793,9796],{"style":152},[60,9794],{"className":9795,"style":157},[156],[60,9797,9799],{"className":9798},[161,162,163,164],[60,9800,9802,9805],{"className":9801},[127,164],[60,9803,87],{"className":9804,"style":171},[127,164],[60,9806,100],{"className":9807,"style":179},[127,178,164],[60,9809,9810,9813],{"style":225},[60,9811],{"className":9812,"style":157},[156],[60,9814],{"className":9815,"style":233},[232],[60,9817,9818,9821],{"style":236},[60,9819],{"className":9820,"style":157},[156],[60,9822,9824],{"className":9823},[161,162,163,164],[60,9825,9827,9830],{"className":9826},[127,164],[60,9828,87],{"className":9829,"style":171},[127,164],[60,9831,562],{"className":9832,"style":639},[127,178,164],[60,9834,213],{"className":9835},[212],[60,9837,9839],{"className":9838},[144],[60,9840,9842],{"className":9841,"style":261},[148],[60,9843],{},[60,9845],{"className":9846},[267,132]," 通常含有 ",[60,9849,9851,9864],{"className":9850},[63],[60,9852,9854],{"className":9853},[67],[69,9855,9856],{"xmlns":71},[73,9857,9858,9862],{},[76,9859,9860],{},[84,9861,100],{},[106,9863,100],{"encoding":108},[60,9865,9867],{"className":9866,"ariaHidden":114},[113],[60,9868,9870,9873],{"className":9869},[118],[60,9871],{"className":9872,"style":299},[122],[60,9874,100],{"className":9875,"style":179},[127,178],"。要计算积分，我们必须先知道",[26,9878,9879,9880],{},"具体的解 ",[60,9881,9883,9907],{"className":9882},[63],[60,9884,9886],{"className":9885},[67],[69,9887,9888],{"xmlns":71},[73,9889,9890,9904],{},[76,9891,9892,9894,9896,9898,9900,9902],{},[84,9893,100],{},[397,9895,448],{},[84,9897,90],{},[397,9899,400],{"stretchy":399},[84,9901,359],{},[397,9903,405],{"stretchy":399},[106,9905,9906],{"encoding":108},"y=\\varphi(x)",[60,9908,9910,9928],{"className":9909,"ariaHidden":114},[113],[60,9911,9913,9916,9919,9922,9925],{"className":9912},[118],[60,9914],{"className":9915,"style":299},[122],[60,9917,100],{"className":9918,"style":179},[127,178],[60,9920],{"className":9921,"style":470},[469],[60,9923,448],{"className":9924},[474],[60,9926],{"className":9927,"style":470},[469],[60,9929,9931,9934,9937,9940,9943],{"className":9930},[118],[60,9932],{"className":9933,"style":418},[122],[60,9935,90],{"className":9936},[127,178],[60,9938,400],{"className":9939},[131],[60,9941,359],{"className":9942},[127,178],[60,9944,405],{"className":9945},[267]," 是什么。",[23,9948,9949,10005,10006,10218,10219,10285,10286,488],{},[26,9950,9951,9952,10004],{},"Step 1: 寻找通过点 ",[60,9953,9955,9977],{"className":9954},[63],[60,9956,9958],{"className":9957},[67],[69,9959,9960],{"xmlns":71},[73,9961,9962,9974],{},[76,9963,9964,9966,9968,9970,9972],{},[397,9965,400],{"stretchy":399},[102,9967,820],{},[397,9969,569],{"separator":114},[102,9971,104],{},[397,9973,405],{"stretchy":399},[106,9975,9976],{"encoding":108},"(1,0)",[60,9978,9980],{"className":9979,"ariaHidden":114},[113],[60,9981,9983,9986,9989,9992,9995,9998,10001],{"className":9982},[118],[60,9984],{"className":9985,"style":418},[122],[60,9987,400],{"className":9988},[131],[60,9990,820],{"className":9991},[127],[60,9993,569],{"className":9994},[649],[60,9996],{"className":9997,"style":653},[469],[60,9999,104],{"className":10000},[127],[60,10002,405],{"className":10003},[267]," 的特解","\n我们观察方程 ",[60,10007,10009,10046],{"className":10008},[63],[60,10010,10012],{"className":10011},[67],[69,10013,10014],{"xmlns":71},[73,10015,10016,10044],{},[76,10017,10018,10032,10034,10036,10038],{},[79,10019,10020,10026],{},[76,10021,10022,10024],{},[84,10023,2173],{"mathvariant":86},[84,10025,100],{},[76,10027,10028,10030],{},[84,10029,2173],{"mathvariant":86},[84,10031,359],{},[397,10033,448],{},[84,10035,9061],{},[397,10037,1465],{},[79,10039,10040,10042],{},[84,10041,100],{},[84,10043,359],{},[106,10045,9072],{"encoding":108},[60,10047,10049,10138],{"className":10048,"ariaHidden":114},[113],[60,10050,10052,10055,10129,10132,10135],{"className":10051},[118],[60,10053],{"className":10054,"style":3836},[122],[60,10056,10058,10061,10126],{"className":10057},[127],[60,10059],{"className":10060},[131,132],[60,10062,10064],{"className":10063},[79],[60,10065,10067,10118],{"className":10066},[139,140],[60,10068,10070,10115],{"className":10069},[144],[60,10071,10073,10090,10098],{"className":10072,"style":149},[148],[60,10074,10075,10078],{"style":152},[60,10076],{"className":10077,"style":157},[156],[60,10079,10081],{"className":10080},[161,162,163,164],[60,10082,10084,10087],{"className":10083},[127,164],[60,10085,2173],{"className":10086},[127,3869,164],[60,10088,359],{"className":10089},[127,178,164],[60,10091,10092,10095],{"style":225},[60,10093],{"className":10094,"style":157},[156],[60,10096],{"className":10097,"style":233},[232],[60,10099,10100,10103],{"style":236},[60,10101],{"className":10102,"style":157},[156],[60,10104,10106],{"className":10105},[161,162,163,164],[60,10107,10109,10112],{"className":10108},[127,164],[60,10110,2173],{"className":10111},[127,3869,164],[60,10113,100],{"className":10114,"style":179},[127,178,164],[60,10116,213],{"className":10117},[212],[60,10119,10121],{"className":10120},[144],[60,10122,10124],{"className":10123,"style":3907},[148],[60,10125],{},[60,10127],{"className":10128},[267,132],[60,10130],{"className":10131,"style":470},[469],[60,10133,448],{"className":10134},[474],[60,10136],{"className":10137,"style":470},[469],[60,10139,10141,10144,10147,10150],{"className":10140},[118],[60,10142],{"className":10143,"style":9171},[122],[60,10145,9061],{"className":10146},[1495],[60,10148],{"className":10149,"style":653},[469],[60,10151,10153,10156,10215],{"className":10152},[127],[60,10154],{"className":10155},[131,132],[60,10157,10159],{"className":10158},[79],[60,10160,10162,10207],{"className":10161},[139,140],[60,10163,10165,10204],{"className":10164},[144],[60,10166,10168,10182,10190],{"className":10167,"style":9196},[148],[60,10169,10170,10173],{"style":152},[60,10171],{"className":10172,"style":157},[156],[60,10174,10176],{"className":10175},[161,162,163,164],[60,10177,10179],{"className":10178},[127,164],[60,10180,359],{"className":10181},[127,178,164],[60,10183,10184,10187],{"style":225},[60,10185],{"className":10186,"style":157},[156],[60,10188],{"className":10189,"style":233},[232],[60,10191,10192,10195],{"style":236},[60,10193],{"className":10194,"style":157},[156],[60,10196,10198],{"className":10197},[161,162,163,164],[60,10199,10201],{"className":10200},[127,164],[60,10202,100],{"className":10203,"style":179},[127,178,164],[60,10205,213],{"className":10206},[212],[60,10208,10210],{"className":10209},[144],[60,10211,10213],{"className":10212,"style":3907},[148],[60,10214],{},[60,10216],{"className":10217},[267,132]," 和初值 ",[60,10220,10222,10246],{"className":10221},[63],[60,10223,10225],{"className":10224},[67],[69,10226,10227],{"xmlns":71},[73,10228,10229,10243],{},[76,10230,10231,10233,10235,10237,10239,10241],{},[84,10232,100],{},[397,10234,400],{"stretchy":399},[102,10236,820],{},[397,10238,405],{"stretchy":399},[397,10240,448],{},[102,10242,104],{},[106,10244,10245],{"encoding":108},"y(1)=0",[60,10247,10249,10276],{"className":10248,"ariaHidden":114},[113],[60,10250,10252,10255,10258,10261,10264,10267,10270,10273],{"className":10251},[118],[60,10253],{"className":10254,"style":418},[122],[60,10256,100],{"className":10257,"style":179},[127,178],[60,10259,400],{"className":10260},[131],[60,10262,820],{"className":10263},[127],[60,10265,405],{"className":10266},[267],[60,10268],{"className":10269,"style":470},[469],[60,10271,448],{"className":10272},[474],[60,10274],{"className":10275,"style":470},[469],[60,10277,10279,10282],{"className":10278},[118],[60,10280],{"className":10281,"style":484},[122],[60,10283,104],{"className":10284},[127],"。\n让我们猜测一个最简单的解：恒为 0 的解，即 ",[60,10287,10289,10308],{"className":10288},[63],[60,10290,10292],{"className":10291},[67],[69,10293,10294],{"xmlns":71},[73,10295,10296,10305],{},[76,10297,10298,10300,10303],{},[84,10299,100],{},[397,10301,10302],{},"≡",[102,10304,104],{},[106,10306,10307],{"encoding":108},"y \\equiv 0",[60,10309,10311,10330],{"className":10310,"ariaHidden":114},[113],[60,10312,10314,10318,10321,10324,10327],{"className":10313},[118],[60,10315],{"className":10316,"style":10317},[122],"height:0.6582em;vertical-align:-0.1944em;",[60,10319,100],{"className":10320,"style":179},[127,178],[60,10322],{"className":10323,"style":470},[469],[60,10325,10302],{"className":10326},[474],[60,10328],{"className":10329,"style":470},[469],[60,10331,10333,10336],{"className":10332},[118],[60,10334],{"className":10335,"style":484},[122],[60,10337,104],{"className":10338},[127],[51,10340,10341,10494,10612],{},[33,10342,10343,10344,488],{},"左边 ",[60,10345,10347,10381],{"className":10346},[63],[60,10348,10350],{"className":10349},[67],[69,10351,10352],{"xmlns":71},[73,10353,10354,10378],{},[76,10355,10356,10362,10364,10366,10368,10374,10376],{},[550,10357,10358,10360],{},[84,10359,100],{},[397,10361,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,10363,448],{},[397,10365,400],{"stretchy":399},[102,10367,104],{},[550,10369,10370,10372],{},[397,10371,405],{"stretchy":399},[397,10373,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,10375,448],{},[102,10377,104],{},[106,10379,10380],{"encoding":108},"y' = (0)' = 0",[60,10382,10384,10431,10485],{"className":10383,"ariaHidden":114},[113],[60,10385,10387,10390,10422,10425,10428],{"className":10386},[118],[60,10388],{"className":10389,"style":586},[122],[60,10391,10393,10396],{"className":10392},[127],[60,10394,100],{"className":10395,"style":179},[127,178],[60,10397,10399],{"className":10398},[183],[60,10400,10402],{"className":10401},[139],[60,10403,10405],{"className":10404},[144],[60,10406,10408],{"className":10407,"style":605},[148],[60,10409,10410,10413],{"style":608},[60,10411],{"className":10412,"style":325},[156],[60,10414,10416],{"className":10415},[161,162,163,164],[60,10417,10419],{"className":10418},[127,164],[60,10420,557],{"className":10421},[127,164],[60,10423],{"className":10424,"style":470},[469],[60,10426,448],{"className":10427},[474],[60,10429],{"className":10430,"style":470},[469],[60,10432,10434,10438,10441,10444,10476,10479,10482],{"className":10433},[118],[60,10435],{"className":10436,"style":10437},[122],"height:1.0019em;vertical-align:-0.25em;",[60,10439,400],{"className":10440},[131],[60,10442,104],{"className":10443},[127],[60,10445,10447,10450],{"className":10446},[267],[60,10448,405],{"className":10449},[267],[60,10451,10453],{"className":10452},[183],[60,10454,10456],{"className":10455},[139],[60,10457,10459],{"className":10458},[144],[60,10460,10462],{"className":10461,"style":605},[148],[60,10463,10464,10467],{"style":608},[60,10465],{"className":10466,"style":325},[156],[60,10468,10470],{"className":10469},[161,162,163,164],[60,10471,10473],{"className":10472},[127,164],[60,10474,557],{"className":10475},[127,164],[60,10477],{"className":10478,"style":470},[469],[60,10480,448],{"className":10481},[474],[60,10483],{"className":10484,"style":470},[469],[60,10486,10488,10491],{"className":10487},[118],[60,10489],{"className":10490,"style":484},[122],[60,10492,104],{"className":10493},[127],[33,10495,10496,10497,488],{},"右边 ",[60,10498,10500,10542],{"className":10499},[63],[60,10501,10503],{"className":10502},[67],[69,10504,10505],{"xmlns":71},[73,10506,10507,10539],{},[76,10508,10509,10511,10513,10515,10517,10519,10521,10523,10525,10527,10529,10531,10533,10535,10537],{},[84,10510,9061],{},[397,10512,1465],{},[397,10514,400],{"stretchy":399},[102,10516,104],{},[84,10518,825],{"mathvariant":86},[84,10520,359],{},[397,10522,405],{"stretchy":399},[397,10524,448],{},[84,10526,9061],{},[397,10528,1465],{},[397,10530,400],{"stretchy":399},[102,10532,104],{},[397,10534,405],{"stretchy":399},[397,10536,448],{},[102,10538,104],{},[106,10540,10541],{"encoding":108},"\\sin(0\u002Fx) = \\sin(0) = 0",[60,10543,10545,10576,10603],{"className":10544,"ariaHidden":114},[113],[60,10546,10548,10551,10554,10557,10561,10564,10567,10570,10573],{"className":10547},[118],[60,10549],{"className":10550,"style":418},[122],[60,10552,9061],{"className":10553},[1495],[60,10555,400],{"className":10556},[131],[60,10558,10560],{"className":10559},[127],"0\u002F",[60,10562,359],{"className":10563},[127,178],[60,10565,405],{"className":10566},[267],[60,10568],{"className":10569,"style":470},[469],[60,10571,448],{"className":10572},[474],[60,10574],{"className":10575,"style":470},[469],[60,10577,10579,10582,10585,10588,10591,10594,10597,10600],{"className":10578},[118],[60,10580],{"className":10581,"style":418},[122],[60,10583,9061],{"className":10584},[1495],[60,10586,400],{"className":10587},[131],[60,10589,104],{"className":10590},[127],[60,10592,405],{"className":10593},[267],[60,10595],{"className":10596,"style":470},[469],[60,10598,448],{"className":10599},[474],[60,10601],{"className":10602,"style":470},[469],[60,10604,10606,10609],{"className":10605},[118],[60,10607],{"className":10608,"style":484},[122],[60,10610,104],{"className":10611},[127],[33,10613,10614,10615,10680,10681,1659,10771],{},"左边 = 右边，且满足初值 ",[60,10616,10618,10641],{"className":10617},[63],[60,10619,10621],{"className":10620},[67],[69,10622,10623],{"xmlns":71},[73,10624,10625,10639],{},[76,10626,10627,10629,10631,10633,10635,10637],{},[84,10628,100],{},[397,10630,400],{"stretchy":399},[102,10632,820],{},[397,10634,405],{"stretchy":399},[397,10636,448],{},[102,10638,104],{},[106,10640,10245],{"encoding":108},[60,10642,10644,10671],{"className":10643,"ariaHidden":114},[113],[60,10645,10647,10650,10653,10656,10659,10662,10665,10668],{"className":10646},[118],[60,10648],{"className":10649,"style":418},[122],[60,10651,100],{"className":10652,"style":179},[127,178],[60,10654,400],{"className":10655},[131],[60,10657,820],{"className":10658},[127],[60,10660,405],{"className":10661},[267],[60,10663],{"className":10664,"style":470},[469],[60,10666,448],{"className":10667},[474],[60,10669],{"className":10670,"style":470},[469],[60,10672,10674,10677],{"className":10673},[118],[60,10675],{"className":10676,"style":484},[122],[60,10678,104],{"className":10679},[127],"。\n因此，此初值问题的解就是 ",[26,10682,10683],{},[60,10684,10686,10714],{"className":10685},[63],[60,10687,10689],{"className":10688},[67],[69,10690,10691],{"xmlns":71},[73,10692,10693,10711],{},[76,10694,10695,10697,10699,10701,10703,10705,10707,10709],{},[84,10696,100],{},[397,10698,448],{},[84,10700,90],{},[397,10702,400],{"stretchy":399},[84,10704,359],{},[397,10706,405],{"stretchy":399},[397,10708,448],{},[102,10710,104],{},[106,10712,10713],{"encoding":108},"y = \\varphi(x) = 0",[60,10715,10717,10735,10762],{"className":10716,"ariaHidden":114},[113],[60,10718,10720,10723,10726,10729,10732],{"className":10719},[118],[60,10721],{"className":10722,"style":299},[122],[60,10724,100],{"className":10725,"style":179},[127,178],[60,10727],{"className":10728,"style":470},[469],[60,10730,448],{"className":10731},[474],[60,10733],{"className":10734,"style":470},[469],[60,10736,10738,10741,10744,10747,10750,10753,10756,10759],{"className":10737},[118],[60,10739],{"className":10740,"style":418},[122],[60,10742,90],{"className":10743},[127,178],[60,10745,400],{"className":10746},[131],[60,10748,359],{"className":10749},[127,178],[60,10751,405],{"className":10752},[267],[60,10754],{"className":10755,"style":470},[469],[60,10757,448],{"className":10758},[474],[60,10760],{"className":10761,"style":470},[469],[60,10763,10765,10768],{"className":10764},[118],[60,10766],{"className":10767,"style":484},[122],[60,10769,104],{"className":10770},[127],[6346,10772,10773],{},"(这一步非常关键！如果不知道解是0，后面的积分就没法算。)",[23,10775,10776,10890,10891,11057,11058,11690,11691,11741,11742],{},[26,10777,5266,10778,10889],{},[60,10779,10781,10806],{"className":10780},[63],[60,10782,10784],{"className":10783},[67],[69,10785,10786],{"xmlns":71},[73,10787,10788,10804],{},[76,10789,10790],{},[79,10791,10792,10798],{},[76,10793,10794,10796],{},[84,10795,87],{"mathvariant":86},[84,10797,562],{},[76,10799,10800,10802],{},[84,10801,87],{"mathvariant":86},[84,10803,100],{},[106,10805,2585],{"encoding":108},[60,10807,10809],{"className":10808,"ariaHidden":114},[113],[60,10810,10812,10815],{"className":10811},[118],[60,10813],{"className":10814,"style":123},[122],[60,10816,10818,10821,10886],{"className":10817},[127],[60,10819],{"className":10820},[131,132],[60,10822,10824],{"className":10823},[79],[60,10825,10827,10878],{"className":10826},[139,140],[60,10828,10830,10875],{"className":10829},[144],[60,10831,10833,10850,10858],{"className":10832,"style":149},[148],[60,10834,10835,10838],{"style":152},[60,10836],{"className":10837,"style":157},[156],[60,10839,10841],{"className":10840},[161,162,163,164],[60,10842,10844,10847],{"className":10843},[127,164],[60,10845,87],{"className":10846,"style":171},[127,164],[60,10848,100],{"className":10849,"style":179},[127,178,164],[60,10851,10852,10855],{"style":225},[60,10853],{"className":10854,"style":157},[156],[60,10856],{"className":10857,"style":233},[232],[60,10859,10860,10863],{"style":236},[60,10861],{"className":10862,"style":157},[156],[60,10864,10866],{"className":10865},[161,162,163,164],[60,10867,10869,10872],{"className":10868},[127,164],[60,10870,87],{"className":10871,"style":171},[127,164],[60,10873,562],{"className":10874,"style":639},[127,178,164],[60,10876,213],{"className":10877},[212],[60,10879,10881],{"className":10880},[144],[60,10882,10884],{"className":10883,"style":261},[148],[60,10885],{},[60,10887],{"className":10888},[267,132]," 并代入特解","\n由 ",[60,10892,10894,10934],{"className":10893},[63],[60,10895,10897],{"className":10896},[67],[69,10898,10899],{"xmlns":71},[73,10900,10901,10931],{},[76,10902,10903,10905,10907,10909,10911,10913,10915,10917,10919,10921,10923,10929],{},[84,10904,562],{},[397,10906,400],{"stretchy":399},[84,10908,359],{},[397,10910,569],{"separator":114},[84,10912,100],{},[397,10914,405],{"stretchy":399},[397,10916,448],{},[84,10918,9061],{},[397,10920,1465],{},[397,10922,400],{"stretchy":399},[79,10924,10925,10927],{},[84,10926,100],{},[84,10928,359],{},[397,10930,405],{"stretchy":399},[106,10932,10933],{"encoding":108},"f(x,y) = \\sin(\\frac{y}{x})",[60,10935,10937,10973],{"className":10936,"ariaHidden":114},[113],[60,10938,10940,10943,10946,10949,10952,10955,10958,10961,10964,10967,10970],{"className":10939},[118],[60,10941],{"className":10942,"style":418},[122],[60,10944,562],{"className":10945,"style":639},[127,178],[60,10947,400],{"className":10948},[131],[60,10950,359],{"className":10951},[127,178],[60,10953,569],{"className":10954},[649],[60,10956],{"className":10957,"style":653},[469],[60,10959,100],{"className":10960,"style":179},[127,178],[60,10962,405],{"className":10963},[267],[60,10965],{"className":10966,"style":470},[469],[60,10968,448],{"className":10969},[474],[60,10971],{"className":10972,"style":470},[469],[60,10974,10976,10980,10983,10986,11054],{"className":10975},[118],[60,10977],{"className":10978,"style":10979},[122],"height:1.095em;vertical-align:-0.345em;",[60,10981,9061],{"className":10982},[1495],[60,10984,400],{"className":10985},[131],[60,10987,10989,10992,11051],{"className":10988},[127],[60,10990],{"className":10991},[131,132],[60,10993,10995],{"className":10994},[79],[60,10996,10998,11043],{"className":10997},[139,140],[60,10999,11001,11040],{"className":11000},[144],[60,11002,11004,11018,11026],{"className":11003,"style":9196},[148],[60,11005,11006,11009],{"style":152},[60,11007],{"className":11008,"style":157},[156],[60,11010,11012],{"className":11011},[161,162,163,164],[60,11013,11015],{"className":11014},[127,164],[60,11016,359],{"className":11017},[127,178,164],[60,11019,11020,11023],{"style":225},[60,11021],{"className":11022,"style":157},[156],[60,11024],{"className":11025,"style":233},[232],[60,11027,11028,11031],{"style":236},[60,11029],{"className":11030,"style":157},[156],[60,11032,11034],{"className":11033},[161,162,163,164],[60,11035,11037],{"className":11036},[127,164],[60,11038,100],{"className":11039,"style":179},[127,178,164],[60,11041,213],{"className":11042},[212],[60,11044,11046],{"className":11045},[144],[60,11047,11049],{"className":11048,"style":3907},[148],[60,11050],{},[60,11052],{"className":11053},[267,132],[60,11055,405],{"className":11056},[267],"，根据链式法则求导：\n",[60,11059,11061,11154],{"className":11060},[63],[60,11062,11064],{"className":11063},[67],[69,11065,11066],{"xmlns":71},[73,11067,11068,11151],{},[76,11069,11070,11084,11086,11089,11091,11103,11105,11115,11127,11129,11135,11137,11139],{},[79,11071,11072,11078],{},[76,11073,11074,11076],{},[84,11075,87],{"mathvariant":86},[84,11077,562],{},[76,11079,11080,11082],{},[84,11081,87],{"mathvariant":86},[84,11083,100],{},[397,11085,448],{},[84,11087,11088],{},"cos",[397,11090,1465],{},[76,11092,11093,11095,11101],{},[397,11094,400],{"fence":114},[79,11096,11097,11099],{},[84,11098,100],{},[84,11100,359],{},[397,11102,405],{"fence":114},[397,11104,2831],{},[79,11106,11107,11109],{},[84,11108,87],{"mathvariant":86},[76,11110,11111,11113],{},[84,11112,87],{"mathvariant":86},[84,11114,100],{},[76,11116,11117,11119,11125],{},[397,11118,400],{"fence":114},[79,11120,11121,11123],{},[84,11122,100],{},[84,11124,359],{},[397,11126,405],{"fence":114},[397,11128,448],{},[79,11130,11131,11133],{},[102,11132,820],{},[84,11134,359],{},[84,11136,11088],{},[397,11138,1465],{},[76,11140,11141,11143,11149],{},[397,11142,400],{"fence":114},[79,11144,11145,11147],{},[84,11146,100],{},[84,11148,359],{},[397,11150,405],{"fence":114},[106,11152,11153],{"encoding":108},"\\frac{\\partial f}{\\partial y} = \\cos\\left(\\frac{y}{x}\\right) \\cdot \\frac{\\partial}{\\partial y}\\left(\\frac{y}{x}\\right) = \\frac{1}{x} \\cos\\left(\\frac{y}{x}\\right)",[60,11155,11157,11246,11351,11523],{"className":11156,"ariaHidden":114},[113],[60,11158,11160,11163,11237,11240,11243],{"className":11159},[118],[60,11161],{"className":11162,"style":123},[122],[60,11164,11166,11169,11234],{"className":11165},[127],[60,11167],{"className":11168},[131,132],[60,11170,11172],{"className":11171},[79],[60,11173,11175,11226],{"className":11174},[139,140],[60,11176,11178,11223],{"className":11177},[144],[60,11179,11181,11198,11206],{"className":11180,"style":149},[148],[60,11182,11183,11186],{"style":152},[60,11184],{"className":11185,"style":157},[156],[60,11187,11189],{"className":11188},[161,162,163,164],[60,11190,11192,11195],{"className":11191},[127,164],[60,11193,87],{"className":11194,"style":171},[127,164],[60,11196,100],{"className":11197,"style":179},[127,178,164],[60,11199,11200,11203],{"style":225},[60,11201],{"className":11202,"style":157},[156],[60,11204],{"className":11205,"style":233},[232],[60,11207,11208,11211],{"style":236},[60,11209],{"className":11210,"style":157},[156],[60,11212,11214],{"className":11213},[161,162,163,164],[60,11215,11217,11220],{"className":11216},[127,164],[60,11218,87],{"className":11219,"style":171},[127,164],[60,11221,562],{"className":11222,"style":639},[127,178,164],[60,11224,213],{"className":11225},[212],[60,11227,11229],{"className":11228},[144],[60,11230,11232],{"className":11231,"style":261},[148],[60,11233],{},[60,11235],{"className":11236},[267,132],[60,11238],{"className":11239,"style":470},[469],[60,11241,448],{"className":11242},[474],[60,11244],{"className":11245,"style":470},[469],[60,11247,11249,11253,11256,11259,11342,11345,11348],{"className":11248},[118],[60,11250],{"className":11251,"style":11252},[122],"height:1.2em;vertical-align:-0.35em;",[60,11254,11088],{"className":11255},[1495],[60,11257],{"className":11258,"style":653},[469],[60,11260,11262,11268,11336],{"className":11261},[2326],[60,11263,11265],{"className":11264,"style":2331},[131,2330],[60,11266,400],{"className":11267},[2335,205],[60,11269,11271,11274,11333],{"className":11270},[127],[60,11272],{"className":11273},[131,132],[60,11275,11277],{"className":11276},[79],[60,11278,11280,11325],{"className":11279},[139,140],[60,11281,11283,11322],{"className":11282},[144],[60,11284,11286,11300,11308],{"className":11285,"style":9196},[148],[60,11287,11288,11291],{"style":152},[60,11289],{"className":11290,"style":157},[156],[60,11292,11294],{"className":11293},[161,162,163,164],[60,11295,11297],{"className":11296},[127,164],[60,11298,359],{"className":11299},[127,178,164],[60,11301,11302,11305],{"style":225},[60,11303],{"className":11304,"style":157},[156],[60,11306],{"className":11307,"style":233},[232],[60,11309,11310,11313],{"style":236},[60,11311],{"className":11312,"style":157},[156],[60,11314,11316],{"className":11315},[161,162,163,164],[60,11317,11319],{"className":11318},[127,164],[60,11320,100],{"className":11321,"style":179},[127,178,164],[60,11323,213],{"className":11324},[212],[60,11326,11328],{"className":11327},[144],[60,11329,11331],{"className":11330,"style":3907},[148],[60,11332],{},[60,11334],{"className":11335},[267,132],[60,11337,11339],{"className":11338,"style":2331},[267,2330],[60,11340,405],{"className":11341},[2335,205],[60,11343],{"className":11344,"style":924},[469],[60,11346,2831],{"className":11347},[928],[60,11349],{"className":11350,"style":924},[469],[60,11352,11354,11357,11428,11431,11514,11517,11520],{"className":11353},[118],[60,11355],{"className":11356,"style":5116},[122],[60,11358,11360,11363,11425],{"className":11359},[127],[60,11361],{"className":11362},[131,132],[60,11364,11366],{"className":11365},[79],[60,11367,11369,11417],{"className":11368},[139,140],[60,11370,11372,11414],{"className":11371},[144],[60,11373,11375,11392,11400],{"className":11374,"style":5135},[148],[60,11376,11377,11380],{"style":152},[60,11378],{"className":11379,"style":157},[156],[60,11381,11383],{"className":11382},[161,162,163,164],[60,11384,11386,11389],{"className":11385},[127,164],[60,11387,87],{"className":11388,"style":171},[127,164],[60,11390,100],{"className":11391,"style":179},[127,178,164],[60,11393,11394,11397],{"style":225},[60,11395],{"className":11396,"style":157},[156],[60,11398],{"className":11399,"style":233},[232],[60,11401,11402,11405],{"style":1105},[60,11403],{"className":11404,"style":157},[156],[60,11406,11408],{"className":11407},[161,162,163,164],[60,11409,11411],{"className":11410},[127,164],[60,11412,87],{"className":11413,"style":171},[127,164],[60,11415,213],{"className":11416},[212],[60,11418,11420],{"className":11419},[144],[60,11421,11423],{"className":11422,"style":261},[148],[60,11424],{},[60,11426],{"className":11427},[267,132],[60,11429],{"className":11430,"style":653},[469],[60,11432,11434,11440,11508],{"className":11433},[2326],[60,11435,11437],{"className":11436,"style":2331},[131,2330],[60,11438,400],{"className":11439},[2335,205],[60,11441,11443,11446,11505],{"className":11442},[127],[60,11444],{"className":11445},[131,132],[60,11447,11449],{"className":11448},[79],[60,11450,11452,11497],{"className":11451},[139,140],[60,11453,11455,11494],{"className":11454},[144],[60,11456,11458,11472,11480],{"className":11457,"style":9196},[148],[60,11459,11460,11463],{"style":152},[60,11461],{"className":11462,"style":157},[156],[60,11464,11466],{"className":11465},[161,162,163,164],[60,11467,11469],{"className":11468},[127,164],[60,11470,359],{"className":11471},[127,178,164],[60,11473,11474,11477],{"style":225},[60,11475],{"className":11476,"style":157},[156],[60,11478],{"className":11479,"style":233},[232],[60,11481,11482,11485],{"style":236},[60,11483],{"className":11484,"style":157},[156],[60,11486,11488],{"className":11487},[161,162,163,164],[60,11489,11491],{"className":11490},[127,164],[60,11492,100],{"className":11493,"style":179},[127,178,164],[60,11495,213],{"className":11496},[212],[60,11498,11500],{"className":11499},[144],[60,11501,11503],{"className":11502,"style":3907},[148],[60,11504],{},[60,11506],{"className":11507},[267,132],[60,11509,11511],{"className":11510,"style":2331},[267,2330],[60,11512,405],{"className":11513},[2335,205],[60,11515],{"className":11516,"style":470},[469],[60,11518,448],{"className":11519},[474],[60,11521],{"className":11522,"style":470},[469],[60,11524,11526,11529,11598,11601,11604,11607],{"className":11525},[118],[60,11527],{"className":11528,"style":11252},[122],[60,11530,11532,11535,11595],{"className":11531},[127],[60,11533],{"className":11534},[131,132],[60,11536,11538],{"className":11537},[79],[60,11539,11541,11587],{"className":11540},[139,140],[60,11542,11544,11584],{"className":11543},[144],[60,11545,11548,11562,11570],{"className":11546,"style":11547},[148],"height:0.8451em;",[60,11549,11550,11553],{"style":152},[60,11551],{"className":11552,"style":157},[156],[60,11554,11556],{"className":11555},[161,162,163,164],[60,11557,11559],{"className":11558},[127,164],[60,11560,359],{"className":11561},[127,178,164],[60,11563,11564,11567],{"style":225},[60,11565],{"className":11566,"style":157},[156],[60,11568],{"className":11569,"style":233},[232],[60,11571,11572,11575],{"style":1105},[60,11573],{"className":11574,"style":157},[156],[60,11576,11578],{"className":11577},[161,162,163,164],[60,11579,11581],{"className":11580},[127,164],[60,11582,820],{"className":11583},[127,164],[60,11585,213],{"className":11586},[212],[60,11588,11590],{"className":11589},[144],[60,11591,11593],{"className":11592,"style":3907},[148],[60,11594],{},[60,11596],{"className":11597},[267,132],[60,11599],{"className":11600,"style":653},[469],[60,11602,11088],{"className":11603},[1495],[60,11605],{"className":11606,"style":653},[469],[60,11608,11610,11616,11684],{"className":11609},[2326],[60,11611,11613],{"className":11612,"style":2331},[131,2330],[60,11614,400],{"className":11615},[2335,205],[60,11617,11619,11622,11681],{"className":11618},[127],[60,11620],{"className":11621},[131,132],[60,11623,11625],{"className":11624},[79],[60,11626,11628,11673],{"className":11627},[139,140],[60,11629,11631,11670],{"className":11630},[144],[60,11632,11634,11648,11656],{"className":11633,"style":9196},[148],[60,11635,11636,11639],{"style":152},[60,11637],{"className":11638,"style":157},[156],[60,11640,11642],{"className":11641},[161,162,163,164],[60,11643,11645],{"className":11644},[127,164],[60,11646,359],{"className":11647},[127,178,164],[60,11649,11650,11653],{"style":225},[60,11651],{"className":11652,"style":157},[156],[60,11654],{"className":11655,"style":233},[232],[60,11657,11658,11661],{"style":236},[60,11659],{"className":11660,"style":157},[156],[60,11662,11664],{"className":11663},[161,162,163,164],[60,11665,11667],{"className":11666},[127,164],[60,11668,100],{"className":11669,"style":179},[127,178,164],[60,11671,213],{"className":11672},[212],[60,11674,11676],{"className":11675},[144],[60,11677,11679],{"className":11678,"style":3907},[148],[60,11680],{},[60,11682],{"className":11683},[267,132],[60,11685,11687],{"className":11686,"style":2331},[267,2330],[60,11688,405],{"className":11689},[2335,205],"\n现在，我们将具体的解 ",[60,11692,11694,11711],{"className":11693},[63],[60,11695,11697],{"className":11696},[67],[69,11698,11699],{"xmlns":71},[73,11700,11701,11709],{},[76,11702,11703,11705,11707],{},[84,11704,100],{},[397,11706,448],{},[102,11708,104],{},[106,11710,453],{"encoding":108},[60,11712,11714,11732],{"className":11713,"ariaHidden":114},[113],[60,11715,11717,11720,11723,11726,11729],{"className":11716},[118],[60,11718],{"className":11719,"style":299},[122],[60,11721,100],{"className":11722,"style":179},[127,178],[60,11724],{"className":11725,"style":470},[469],[60,11727,448],{"className":11728},[474],[60,11730],{"className":11731,"style":470},[469],[60,11733,11735,11738],{"className":11734},[118],[60,11736],{"className":11737,"style":484},[122],[60,11739,104],{"className":11740},[127]," 代入上式：\n",[60,11743,11745,11824],{"className":11744},[63],[60,11746,11748],{"className":11747},[67],[69,11749,11750],{"xmlns":71},[73,11751,11752,11821],{},[76,11753,11754,11783,11785,11791,11793,11795,11797,11799,11801,11803,11809,11811,11813,11815],{},[96,11755,11756,11775],{},[76,11757,11758,11772],{},[79,11759,11760,11766],{},[76,11761,11762,11764],{},[84,11763,87],{"mathvariant":86},[84,11765,562],{},[76,11767,11768,11770],{},[84,11769,87],{"mathvariant":86},[84,11771,100],{},[397,11773,11774],{"fence":114},"∣",[76,11776,11777,11779,11781],{},[84,11778,100],{},[397,11780,448],{},[102,11782,104],{},[397,11784,448],{},[79,11786,11787,11789],{},[102,11788,820],{},[84,11790,359],{},[84,11792,11088],{},[397,11794,1465],{},[397,11796,400],{"stretchy":399},[102,11798,104],{},[397,11800,405],{"stretchy":399},[397,11802,448],{},[79,11804,11805,11807],{},[102,11806,820],{},[84,11808,359],{},[397,11810,2831],{},[102,11812,820],{},[397,11814,448],{},[79,11816,11817,11819],{},[102,11818,820],{},[84,11820,359],{},[106,11822,11823],{"encoding":108},"\\left. \\frac{\\partial f}{\\partial y} \\right|_{y=0} = \\frac{1}{x} \\cos(0) = \\frac{1}{x} \\cdot 1 = 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e":12256},[127,164],[60,12258,359],{"className":12259},[127,178,164],[60,12261,12262,12265],{"style":225},[60,12263],{"className":12264,"style":157},[156],[60,12266],{"className":12267,"style":233},[232],[60,12269,12270,12273],{"style":1105},[60,12271],{"className":12272,"style":157},[156],[60,12274,12276],{"className":12275},[161,162,163,164],[60,12277,12279],{"className":12278},[127,164],[60,12280,820],{"className":12281},[127,164],[60,12283,213],{"className":12284},[212],[60,12286,12288],{"className":12287},[144],[60,12289,12291],{"className":12290,"style":3907},[148],[60,12292],{},[60,12294],{"className":12295},[267,132],[23,12297,12298,12452,12453,12545,12546,12911,12912,13010,13011,13496,13497,13721,13724,13725],{},[26,12299,6456,12300],{},[60,12301,12303,12332],{"className":12302},[63],[60,12304,12306],{"className":12305},[67],[69,12307,12308],{"xmlns":71},[73,12309,12310,12330],{},[76,12311,12312],{},[79,12313,12314,12320],{},[76,12315,12316,12318],{},[84,12317,87],{"mathvariant":86},[84,12319,100],{},[76,12321,12322,12324],{},[84,12323,87],{"mathvariant":86},[96,12325,12326,12328],{},[84,12327,100],{},[102,12329,104],{},[106,12331,9434],{"encoding":108},[60,12333,12335],{"className":12334,"ariaHidden":114},[113],[60,12336,12338,12341],{"className":12337},[118],[60,12339],{"className":12340,"style":123},[122],[60,12342,12344,12347,12449],{"className":12343},[127],[60,12345],{"className":12346},[131,132],[60,12348,12350],{"className":12349},[79],[60,12351,12353,12441],{"className":12352},[139,140],[60,12354,12356,12438],{"className":12355},[144],[60,12357,12359,12413,12421],{"className":12358,"style":149},[148],[60,12360,12361,12364],{"style":152},[60,12362],{"className":12363,"style":157},[156],[60,12365,12367],{"className":12366},[161,162,163,164],[60,12368,12370,12373],{"className":12369},[127,164],[60,12371,87],{"className":12372,"style":171},[127,164],[60,12374,12376,12379],{"className":12375},[127,164],[60,12377,100],{"className":12378,"style":179},[127,178,164],[60,12380,12382],{"className":12381},[183],[60,12383,12385,12405],{"className":12384},[139,140],[60,12386,12388,12402],{"className":12387},[144],[60,12389,12391],{"className":12390,"style":193},[148],[60,12392,12393,12396],{"style":196},[60,12394],{"className":12395,"style":200},[156],[60,12397,12399],{"className":12398},[161,204,205,164],[60,12400,104],{"className":12401},[127,164],[60,12403,213],{"className":12404},[212],[60,12406,12408],{"className":12407},[144],[60,12409,12411],{"className":12410,"style":220},[148],[60,12412],{},[60,12414,12415,12418],{"style":225},[60,12416],{"className":12417,"style":157},[156],[60,12419],{"className":12420,"style":233},[232],[60,12422,12423,12426],{"style":236},[60,12424],{"className":12425,"style":157},[156],[60,12427,12429],{"className":12428},[161,162,163,164],[60,12430,12432,12435],{"className":12431},[127,164],[60,12433,87],{"className":12434,"style":171},[127,164],[60,12436,100],{"className":12437,"style":179},[127,178,164],[60,12439,213],{"className":12440},[212],[60,12442,12444],{"className":12443},[144],[60,12445,12447],{"className":12446,"style":261},[148],[60,12448],{},[60,12450],{"className":12451},[267,132],"\n利用公式 (3.18)，注意下限 ",[60,12454,12456,12478],{"className":12455},[63],[60,12457,12459],{"className":12458},[67],[69,12460,12461],{"xmlns":71},[73,12462,12463,12475],{},[76,12464,12465,12471,12473],{},[96,12466,12467,12469],{},[84,12468,359],{},[102,12470,104],{},[397,12472,448],{},[102,12474,820],{},[106,12476,12477],{"encoding":108},"x_0 = 1",[60,12479,12481,12536],{"className":12480,"ariaHidden":114},[113],[60,12482,12484,12487,12527,12530,12533],{"className":12483},[118],[60,12485],{"className":12486,"style":2734},[122],[60,12488,12490,12493],{"className":12489},[127],[60,12491,359],{"className":12492},[127,178],[60,12494,12496],{"className":12495},[183],[60,12497,12499,12519],{"className":12498},[139,140],[60,12500,12502,12516],{"className":12501},[144],[60,12503,12505],{"className":12504,"style":318},[148],[60,12506,12507,12510],{"style":1940},[60,12508],{"className":12509,"style":325},[156],[60,12511,12513],{"className":12512},[161,162,163,164],[60,12514,104],{"className":12515},[127,164],[60,12517,213],{"className":12518},[212],[60,12520,12522],{"className":12521},[144],[60,12523,12525],{"className":12524,"style":341},[148],[60,12526],{},[60,12528],{"className":12529,"style":470},[469],[60,12531,448],{"className":12532},[474],[60,12534],{"className":12535,"style":470},[469],[60,12537,12539,12542],{"className":12538},[118],[60,12540],{"className":12541,"style":484},[122],[60,12543,820],{"className":12544},[127],"：\n",[60,12547,12549,12617],{"className":12548},[63],[60,12550,12552],{"className":12551},[67],[69,12553,12554],{"xmlns":71},[73,12555,12556,12614],{},[76,12557,12558,12576,12578,12580,12582],{},[79,12559,12560,12566],{},[76,12561,12562,12564],{},[84,12563,87],{"mathvariant":86},[84,12565,100],{},[76,12567,12568,12570],{},[84,12569,87],{"mathvariant":86},[96,12571,12572,12574],{},[84,12573,100],{},[102,12575,104],{},[397,12577,448],{},[84,12579,2119],{},[397,12581,1465],{},[76,12583,12584,12586,12594,12608,12610,12612],{},[397,12585,400],{"fence":114},[2127,12587,12588,12590,12592],{},[397,12589,2131],{},[102,12591,820],{},[84,12593,359],{},[79,12595,12596,12602],{},[76,12597,12598,12600],{},[84,12599,87],{"mathvariant":86},[84,12601,562],{},[76,12603,12604,12606],{},[84,12605,87],{"mathvariant":86},[84,12607,100],{},[84,12609,2173],{},[84,12611,2152],{},[397,12613,405],{"fence":114},[106,12615,12616],{"encoding":108},"\\frac{\\partial y}{\\partial y_0} = \\exp\\left( \\int_{1}^x \\frac{\\partial f}{\\partial y} dt \\right)",[60,12618,12620,12746],{"className":12619,"ariaHidden":114},[113],[60,12621,12623,12626,12737,12740,12743],{"className":12622},[118],[60,12624],{"className":12625,"style":123},[122],[60,12627,12629,12632,12734],{"className":12628},[127],[60,12630],{"className":12631},[131,132],[60,12633,12635],{"className":12634},[79],[60,12636,12638,12726],{"className":12637},[139,140],[60,12639,12641,12723],{"className":12640},[144],[60,12642,12644,12698,12706],{"className":12643,"style":149},[148],[60,12645,12646,12649],{"style":152},[60,12647],{"className":12648,"style":157},[156],[60,12650,12652],{"className":12651},[161,162,163,164],[60,12653,12655,12658],{"className":12654},[127,164],[60,12656,87],{"className":12657,"style":171},[127,164],[60,12659,12661,12664],{"className":12660},[127,164],[60,12662,100],{"className":12663,"style":179},[127,178,164],[60,12665,12667],{"className":12666},[183],[60,12668,12670,12690],{"className":12669},[139,140],[60,12671,12673,12687],{"className":12672},[144],[60,12674,12676],{"className":12675,"style":193},[148],[60,12677,12678,12681],{"style":196},[60,12679],{"className":12680,"style":200},[156],[60,12682,12684],{"className":12683},[161,204,205,164],[60,12685,104],{"className":12686},[127,164],[60,12688,213],{"className":12689},[212],[60,12691,12693],{"className":12692},[144],[60,12694,12696],{"className":12695,"style":220},[148],[60,12697],{},[60,12699,12700,12703],{"style":225},[60,12701],{"className":12702,"style":157},[156],[60,12704],{"className":12705,"style":233},[232],[60,12707,12708,12711],{"style":236},[60,12709],{"className":12710,"style":157},[156],[60,12712,12714],{"className":12713},[161,162,163,164],[60,12715,12717,12720],{"className":12716},[127,164],[60,12718,87],{"className":12719,"style":171},[127,164],[60,12721,100],{"className":12722,"style":179},[127,178,164],[60,12724,213],{"className":12725},[212],[60,12727,12729],{"className":12728},[144],[60,12730,12732],{"className":12731,"style":261},[148],[60,12733],{},[60,12735],{"className":12736},[267,132],[60,12738],{"className":12739,"style":470},[469],[60,12741,448],{"className":12742},[474],[60,12744],{"className":12745,"style":470},[469],[60,12747,12749,12752,12755,12758],{"className":12748},[118],[60,12750],{"className":12751,"style":2316},[122],[60,12753,2119],{"className":12754},[1495],[60,12756],{"className":12757,"style":653},[469],[60,12759,12761,12767,12822,12825,12899,12902,12905],{"className":12760},[2326],[60,12762,12764],{"className":12763,"style":2331},[131,2330],[60,12765,400],{"className":12766},[2335,2336],[60,12768,12770,12773],{"className":12769},[1495],[60,12771,2131],{"className":12772,"style":2345},[1495,2343,2344],[60,12774,12776],{"className":12775},[183],[60,12777,12779,12813],{"className":12778},[139,140],[60,12780,12782,12810],{"className":12781},[144],[60,12783,12785,12799],{"className":12784,"style":2358},[148],[60,12786,12787,12790],{"style":2361},[60,12788],{"className":12789,"style":325},[156],[60,12791,12793],{"className":12792},[161,162,163,164],[60,12794,12796],{"className":12795},[127,164],[60,12797,820],{"className":12798},[127,164],[60,12800,12801,12804],{"style":2414},[60,12802],{"className":12803,"style":325},[156],[60,12805,12807],{"className":12806},[161,162,163,164],[60,12808,359],{"className":12809},[127,178,164],[60,12811,213],{"className":12812},[212],[60,12814,12816],{"className":12815},[144],[60,12817,12820],{"className":12818,"style":12819},[148],"height:0.3558em;",[60,12821],{},[60,12823],{"className":12824,"style":653},[469],[60,12826,12828,12831,12896],{"className":12827},[127],[60,12829],{"className":12830},[131,132],[60,12832,12834],{"className":12833},[79],[60,12835,12837,12888],{"className":12836},[139,140],[60,12838,12840,12885],{"className":12839},[144],[60,12841,12843,12860,12868],{"className":12842,"style":149},[148],[60,12844,12845,12848],{"style":152},[60,12846],{"className":12847,"style":157},[156],[60,12849,12851],{"className":12850},[161,162,163,164],[60,12852,12854,12857],{"className":12853},[127,164],[60,12855,87],{"className":12856,"style":171},[127,164],[60,12858,100],{"className":12859,"style":179},[127,178,164],[60,12861,12862,12865],{"style":225},[60,12863],{"className":12864,"style":157},[156],[60,12866],{"className":12867,"style":233},[232],[60,12869,12870,12873],{"style":236},[60,12871],{"className":12872,"style":157},[156],[60,12874,12876],{"className":12875},[161,162,163,164],[60,12877,12879,12882],{"className":12878},[127,164],[60,12880,87],{"className":12881,"style":171},[127,164],[60,12883,562],{"className":12884,"style":639},[127,178,164],[60,12886,213],{"className":12887},[212],[60,12889,12891],{"className":12890},[144],[60,12892,12894],{"className":12893,"style":261},[148],[60,12895],{},[60,12897],{"className":12898},[267,132],[60,12900,2173],{"className":12901},[127,178],[60,12903,2152],{"className":12904},[127,178],[60,12906,12908],{"className":12907,"style":2331},[267,2330],[60,12909,405],{"className":12910},[2335,2336],"\n将 Step 2 算出的 ",[60,12913,12915,12933],{"className":12914},[63],[60,12916,12918],{"className":12917},[67],[69,12919,12920],{"xmlns":71},[73,12921,12922,12930],{},[76,12923,12924],{},[79,12925,12926,12928],{},[102,12927,820],{},[84,12929,2152],{},[106,12931,12932],{"encoding":108},"\\frac{1}{t}",[60,12934,12936],{"className":12935,"ariaHidden":114},[113],[60,12937,12939,12942],{"className":12938},[118],[60,12940],{"className":12941,"style":12028},[122],[60,12943,12945,12948,13007],{"className":12944},[127],[60,12946],{"className":12947},[131,132],[60,12949,12951],{"className":12950},[79],[60,12952,12954,12999],{"className":12953},[139,140],[60,12955,12957,12996],{"className":12956},[144],[60,12958,12960,12974,12982],{"className":12959,"style":11547},[148],[60,12961,12962,12965],{"style":152},[60,12963],{"className":12964,"style":157},[156],[60,12966,12968],{"className":12967},[161,162,163,164],[60,12969,12971],{"className":12970},[127,164],[60,12972,2152],{"className":12973},[127,178,164],[60,12975,12976,12979],{"style":225},[60,12977],{"className":12978,"style":157},[156],[60,12980],{"className":12981,"style":233},[232],[60,12983,12984,12987],{"style":1105},[60,12985],{"className":12986,"style":157},[156],[60,12988,12990],{"className":12989},[161,162,163,164],[60,12991,12993],{"className":12992},[127,164],[60,12994,820],{"className":12995},[127,164],[60,12997,213],{"className":12998},[212],[60,13000,13002],{"className":13001},[144],[60,13003,13005],{"className":13004,"style":3907},[148],[60,13006],{},[60,13008],{"className":13009},[267,132]," 代入积分：\n",[60,13012,13014,13110],{"className":13013},[63],[60,13015,13017],{"className":13016},[67],[69,13018,13019],{"xmlns":71},[73,13020,13021,13107],{},[76,13022,13023,13031,13037,13039,13041,13043,13045,13047,13049,13051,13053,13061,13063,13065,13067,13069,13071,13073,13075,13077,13079,13081,13083,13085,13087,13089,13092,13094,13098,13100,13103,13105],{},[2127,13024,13025,13027,13029],{},[397,13026,2131],{},[102,13028,820],{},[84,13030,359],{},[79,13032,13033,13035],{},[102,13034,820],{},[84,13036,2152],{},[84,13038,2173],{},[84,13040,2152],{},[397,13042,448],{},[84,13044,1462],{},[397,13046,1465],{},[84,13048,11774],{"mathvariant":86},[84,13050,2152],{},[84,13052,11774],{"mathvariant":86},[2127,13054,13055,13057,13059],{},[397,13056,11774],{"fence":399,"stretchy":114,"minsize":11949,"maxsize":11949},[102,13058,820],{},[84,13060,359],{},[397,13062,448],{},[84,13064,1462],{},[397,13066,1465],{},[84,13068,11774],{"mathvariant":86},[84,13070,359],{},[84,13072,11774],{"mathvariant":86},[397,13074,817],{},[84,13076,1462],{},[397,13078,1465],{},[102,13080,820],{},[397,13082,448],{},[84,13084,1462],{},[397,13086,1465],{},[84,13088,359],{},[469,13090],{"width":13091},"1em",[397,13093,400],{"stretchy":399},[13095,13096,13097],"mtext",{},"考虑 ",[84,13099,359],{},[397,13101,13102],{},">",[102,13104,104],{},[397,13106,405],{"stretchy":399},[106,13108,13109],{"encoding":108},"\\int_{1}^x \\frac{1}{t} dt = \\ln|t| \\Big|_{1}^x = \\ln|x| - \\ln 1 = \\ln x \\quad (\\text{考虑 } x>0)",[60,13111,13113,13260,13382,13412,13437,13484],{"className":13112,"ariaHidden":114},[113],[60,13114,13116,13120,13174,13177,13245,13248,13251,13254,13257],{"className":13115},[118],[60,13117],{"className":13118,"style":13119},[122],"height:1.2151em;vertical-align:-0.3558em;",[60,13121,13123,13126],{"className":13122},[1495],[60,13124,2131],{"className":13125,"style":2345},[1495,2343,2344],[60,13127,13129],{"className":13128},[183],[60,13130,13132,13166],{"className":13131},[139,140],[60,13133,13135,13163],{"className":13134},[144],[60,13136,13138,13152],{"className":13137,"style":2358},[148],[60,13139,13140,13143],{"style":2361},[60,13141],{"className":13142,"style":325},[156],[60,13144,13146],{"className":13145},[161,162,163,164],[60,13147,13149],{"className":13148},[127,164],[60,13150,820],{"className":13151},[127,164],[60,13153,13154,13157],{"style":2414},[60,13155],{"className":13156,"style":325},[156],[60,13158,13160],{"className":13159},[161,162,163,164],[60,13161,359],{"className":13162},[127,178,164],[60,13164,213],{"className":13165},[212],[60,13167,13169],{"className":13168},[144],[60,13170,13172],{"className":13171,"style":12819},[148],[60,13173],{},[60,13175],{"className":13176,"style":653},[469],[60,13178,13180,13183,13242],{"className":13179},[127],[60,13181],{"className":13182},[131,132],[60,13184,13186],{"className":13185},[79],[60,13187,13189,13234],{"className":13188},[139,140],[60,13190,13192,13231],{"className":13191},[144],[60,13193,13195,13209,13217],{"className":13194,"style":11547},[148],[60,13196,13197,13200],{"style":152},[60,13198],{"className":13199,"style":157},[156],[60,13201,13203],{"className":13202},[161,162,163,164],[60,13204,13206],{"className":13205},[127,164],[60,13207,2152],{"className":13208},[127,178,164],[60,13210,13211,13214],{"style":225},[60,13212],{"className":13213,"style":157},[156],[60,13215],{"className":13216,"style":233},[232],[60,13218,13219,13222],{"style":1105},[60,13220],{"className":13221,"style":157},[156],[60,13223,13225],{"className":13224},[161,162,163,164],[60,13226,13228],{"className":13227},[127,164],[60,13229,820],{"className":13230},[127,164],[60,13232,213],{"className":13233},[212],[60,13235,13237],{"className":13236},[144],[60,13238,13240],{"className":13239,"style":3907},[148],[60,13241],{},[60,13243],{"className":13244},[267,132],[60,13246,2173],{"className":13247},[127,178],[60,13249,2152],{"className":13250},[127,178],[60,13252],{"className":13253,"style":470},[469],[60,13255,448],{"className":13256},[474],[60,13258],{"className":13259,"style":470},[469],[60,13261,13263,13267,13270,13273,13276,13279,13282,13373,13376,13379],{"className":13262},[118],[60,13264],{"className":13265,"style":13266},[122],"height:1.904em;vertical-align:-0.6997em;",[60,13268,1462],{"className":13269},[1495],[60,13271],{"className":13272,"style":653},[469],[60,13274,11774],{"className":13275},[127],[60,13277,2152],{"className":13278},[127,178],[60,13280,11774],{"className":13281},[127],[60,13283,13285,13322],{"className":13284},[127],[60,13286,13288],{"className":13287},[127],[60,13289,13291],{"className":13290},[2335,11923],[60,13292,13294,13314],{"className":13293},[139,140],[60,13295,13297,13311],{"className":13296},[144],[60,13298,13300],{"className":13299,"style":11933},[148],[60,13301,13302,13305],{"style":11936},[60,13303],{"className":13304,"style":11940},[156],[60,13306,13307],{"style":11943},[11945,13308,13309],{"xmlns":11947,"width":11948,"height":11949,"viewBox":11950},[11952,13310],{"d":11954},[60,13312,213],{"className":13313},[212],[60,13315,13317],{"className":13316},[144],[60,13318,13320],{"className":13319,"style":11964},[148],[60,13321],{},[60,13323,13325],{"className":13324},[183],[60,13326,13328,13364],{"className":13327},[139,140],[60,13329,13331,13361],{"className":13330},[144],[60,13332,13335,13349],{"className":13333,"style":13334},[148],"height:1.2043em;",[60,13336,13337,13340],{"style":11982},[60,13338],{"className":13339,"style":325},[156],[60,13341,13343],{"className":13342},[161,162,163,164],[60,13344,13346],{"className":13345},[127,164],[60,13347,820],{"className":13348},[127,164],[60,13350,13352,13355],{"style":13351},"top:-3.6029em;margin-right:0.05em;",[60,13353],{"className":13354,"style":325},[156],[60,13356,13358],{"className":13357},[161,162,163,164],[60,13359,359],{"className":13360},[127,178,164],[60,13362,213],{"className":13363},[212],[60,13365,13367],{"className":13366},[144],[60,13368,13371],{"className":13369,"style":13370},[148],"height:0.6997em;",[60,13372],{},[60,13374],{"className":13375,"style":470},[469],[60,13377,448],{"className":13378},[474],[60,13380],{"className":13381,"style":470},[469],[60,13383,13385,13388,13391,13394,13397,13400,13403,13406,13409],{"className":13384},[118],[60,13386],{"className":13387,"style":418},[122],[60,13389,1462],{"className":13390},[1495],[60,13392],{"className":13393,"style":653},[469],[60,13395,11774],{"className":13396},[127],[60,13398,359],{"className":13399},[127,178],[60,13401,11774],{"className":13402},[127],[60,13404],{"className":13405,"style":924},[469],[60,13407,817],{"className":13408},[928],[60,13410],{"className":13411,"style":924},[469],[60,13413,13415,13419,13422,13425,13428,13431,13434],{"className":13414},[118],[60,13416],{"className":13417,"style":13418},[122],"height:0.6944em;",[60,13420,1462],{"className":13421},[1495],[60,13423],{"className":13424,"style":653},[469],[60,13426,820],{"className":13427},[127],[60,13429],{"className":13430,"style":470},[469],[60,13432,448],{"className":13433},[474],[60,13435],{"className":13436,"style":470},[469],[60,13438,13440,13443,13446,13449,13452,13456,13459,13472,13475,13478,13481],{"className":13439},[118],[60,13441],{"className":13442,"style":418},[122],[60,13444,1462],{"className":13445},[1495],[60,13447],{"className":13448,"style":653},[469],[60,13450,359],{"className":13451},[127,178],[60,13453],{"className":13454,"style":13455},[469],"margin-right:1em;",[60,13457,400],{"className":13458},[131],[60,13460,13463,13468],{"className":13461},[127,13462],"text",[60,13464,13467],{"className":13465},[127,13466],"cjk_fallback","考虑",[60,13469,13471],{"className":13470},[127]," ",[60,13473,359],{"className":13474},[127,178],[60,13476],{"className":13477,"style":470},[469],[60,13479,13102],{"className":13480},[474],[60,13482],{"className":13483,"style":470},[469],[60,13485,13487,13490,13493],{"className":13486},[118],[60,13488],{"className":13489,"style":418},[122],[60,13491,104],{"className":13492},[127],[60,13494,405],{"className":13495},[267],"\n所以：\n",[60,13498,13500,13550],{"className":13499},[63],[60,13501,13503],{"className":13502},[67],[69,13504,13505],{"xmlns":71},[73,13506,13507,13547],{},[76,13508,13509,13527,13529,13531,13533,13535,13537,13539,13541,13543,13545],{},[79,13510,13511,13517],{},[76,13512,13513,13515],{},[84,13514,87],{"mathvariant":86},[84,13516,100],{},[76,13518,13519,13521],{},[84,13520,87],{"mathvariant":86},[96,13522,13523,13525],{},[84,13524,100],{},[102,13526,104],{},[397,13528,448],{},[84,13530,2119],{},[397,13532,1465],{},[397,13534,400],{"stretchy":399},[84,13536,1462],{},[397,13538,1465],{},[84,13540,359],{},[397,13542,405],{"stretchy":399},[397,13544,448],{},[84,13546,359],{},[106,13548,13549],{"encoding":108},"\\frac{\\partial y}{\\partial y_0} = \\exp(\\ln x) = x",[60,13551,13553,13679,13712],{"className":13552,"ariaHidden":114},[113],[60,13554,13556,13559,13670,13673,13676],{"className":13555},[118],[60,13557],{"className":13558,"style":123},[122],[60,13560,13562,13565,13667],{"className":13561},[127],[60,13563],{"className":13564},[131,132],[60,13566,13568],{"className":13567},[79],[60,13569,13571,13659],{"className":13570},[139,140],[60,13572,13574,13656],{"className":13573},[144],[60,13575,13577,13631,13639],{"className":13576,"style":149},[148],[60,13578,13579,13582],{"style":152},[60,13580],{"className":13581,"style":157},[156],[60,13583,13585],{"className":13584},[161,162,163,164],[60,13586,13588,13591],{"className":13587},[127,164],[60,13589,87],{"className":13590,"style":171},[127,164],[60,13592,13594,13597],{"className":13593},[127,164],[60,13595,100],{"className":13596,"style":179},[127,178,164],[60,13598,13600],{"className":13599},[183],[60,13601,13603,13623],{"className":13602},[139,140],[60,13604,13606,13620],{"className":13605},[144],[60,13607,13609],{"className":13608,"style":193},[148],[60,13610,13611,13614],{"style":196},[60,13612],{"className":13613,"style":200},[156],[60,13615,13617],{"className":13616},[161,204,205,164],[60,13618,104],{"className":13619},[127,164],[60,13621,213],{"className":13622},[212],[60,13624,13626],{"className":13625},[144],[60,13627,13629],{"className":13628,"style":220},[148],[60,13630],{},[60,13632,13633,13636],{"style":225},[60,13634],{"className":13635,"style":157},[156],[60,13637],{"className":13638,"style":233},[232],[60,13640,13641,13644],{"style":236},[60,13642],{"className":13643,"style":157},[156],[60,13645,13647],{"className":13646},[161,162,163,164],[60,13648,13650,13653],{"className":13649},[127,164],[60,13651,87],{"className":13652,"style":171},[127,164],[60,13654,100],{"className":13655,"style":179},[127,178,164],[60,13657,213],{"className":13658},[212],[60,13660,13662],{"className":13661},[144],[60,13663,13665],{"className":13664,"style":261},[148],[60,13666],{},[60,13668],{"className":13669},[267,132],[60,13671],{"className":13672,"style":470},[469],[60,13674,448],{"className":13675},[474],[60,13677],{"className":13678,"style":470},[469],[60,13680,13682,13685,13688,13691,13694,13697,13700,13703,13706,13709],{"className":13681},[118],[60,13683],{"className":13684,"style":418},[122],[60,13686,2119],{"className":13687},[1495],[60,13689,400],{"className":13690},[131],[60,13692,1462],{"className":13693},[1495],[60,13695],{"className":13696,"style":653},[469],[60,13698,359],{"className":13699},[127,178],[60,13701,405],{"className":13702},[267],[60,13704],{"className":13705,"style":470},[469],[60,13707,448],{"className":13708},[474],[60,13710],{"className":13711,"style":470},[469],[60,13713,13715,13718],{"className":13714},[118],[60,13716],{"className":13717,"style":371},[122],[60,13719,359],{"className":13720},[127,178],[26,13722,13723],{},"结论："," ",[60,13726,13728,13762],{"className":13727},[63],[60,13729,13731],{"className":13730},[67],[69,13732,13733],{"xmlns":71},[73,13734,13735,13759],{},[76,13736,13737,13755,13757],{},[79,13738,13739,13745],{},[76,13740,13741,13743],{},[84,13742,87],{"mathvariant":6025},[84,13744,100],{"mathvariant":6025},[76,13746,13747,13749],{},[84,13748,87],{"mathvariant":6025},[96,13750,13751,13753],{},[84,13752,100],{"mathvariant":6025},[102,13754,104],{"mathvariant":6025},[397,13756,448],{},[84,13758,359],{"mathvariant":6025},[106,13760,13761],{"encoding":108},"\\mathbf{\\frac{\\partial y}{\\partial y_0} = x}",[60,13763,13765],{"className":13764,"ariaHidden":114},[113],[60,13766,13768,13771],{"className":13767},[118],[60,13769],{"className":13770,"style":123},[122],[60,13772,13774,13883,13886,13889,13892],{"className":13773},[127],[60,13775,13777,13780,13880],{"className":13776},[127],[60,13778],{"className":13779},[131,132],[60,13781,13783],{"className":13782},[79],[60,13784,13786,13872],{"className":13785},[139,140],[60,13787,13789,13869],{"className":13788},[144],[60,13790,13792,13846,13854],{"className":13791,"style":149},[148],[60,13793,13794,13797],{"style":152},[60,13795],{"className":13796,"style":157},[156],[60,13798,13800],{"className":13799},[161,162,163,164],[60,13801,13803,13806],{"className":13802},[127,164],[60,13804,87],{"className":13805,"style":6122},[127,6121,164],[60,13807,13809,13812],{"className":13808},[127,164],[60,13810,100],{"className":13811,"style":6129},[127,6121,164],[60,13813,13815],{"className":13814},[183],[60,13816,13818,13838],{"className":13817},[139,140],[60,13819,13821,13835],{"className":13820},[144],[60,13822,13824],{"className":13823,"style":193},[148],[60,13825,13826,13829],{"style":6144},[60,13827],{"className":13828,"style":200},[156],[60,13830,13832],{"className":13831},[161,204,205,164],[60,13833,104],{"className":13834},[127,6121,164],[60,13836,213],{"className":13837},[212],[60,13839,13841],{"className":13840},[144],[60,13842,13844],{"className":13843,"style":220},[148],[60,13845],{},[60,13847,13848,13851],{"style":225},[60,13849],{"className":13850,"style":157},[156],[60,13852],{"className":13853,"style":233},[232],[60,13855,13856,13859],{"style":236},[60,13857],{"className":13858,"style":157},[156],[60,13860,13862],{"className":13861},[161,162,163,164],[60,13863,13865],{"className":13864},[127,164],[60,13866,13868],{"className":13867,"style":6129},[127,6121,164],"∂y",[60,13870,213],{"className":13871},[212],[60,13873,13875],{"className":13874},[144],[60,13876,13878],{"className":13877,"style":261},[148],[60,13879],{},[60,13881],{"className":13882},[267,132],[60,13884],{"className":13885,"style":470},[469],[60,13887,448],{"className":13888},[474],[60,13890],{"className":13891,"style":470},[469],[60,13893,359],{"className":13894},[127,6121],[23,13896,13897,14051,14052,4770,14488,14626,14627,12545,14684,14885,14886,15110,13724,15112],{},[26,13898,8355,13899],{},[60,13900,13902,13931],{"className":13901},[63],[60,13903,13905],{"className":13904},[67],[69,13906,13907],{"xmlns":71},[73,13908,13909,13929],{},[76,13910,13911],{},[79,13912,13913,13919],{},[76,13914,13915,13917],{},[84,13916,87],{"mathvariant":86},[84,13918,100],{},[76,13920,13921,13923],{},[84,13922,87],{"mathvariant":86},[96,13924,13925,13927],{},[84,13926,359],{},[102,13928,104],{},[106,13930,9280],{"encoding":108},[60,13932,13934],{"className":13933,"ariaHidden":114},[113],[60,13935,13937,13940],{"className":13936},[118],[60,13938],{"className":13939,"style":2862},[122],[60,13941,13943,13946,14048],{"className":13942},[127],[60,13944],{"className":13945},[131,132],[60,13947,13949],{"className":13948},[79],[60,13950,13952,14040],{"className":13951},[139,140],[60,13953,13955,14037],{"className":13954},[144],[60,13956,13958,14012,14020],{"className":13957,"style":149},[148],[60,13959,13960,13963],{"style":152},[60,13961],{"className":13962,"style":157},[156],[60,13964,13966],{"className":13965},[161,162,163,164],[60,13967,13969,13972],{"className":13968},[127,164],[60,13970,87],{"className":13971,"style":171},[127,164],[60,13973,13975,13978],{"className":13974},[127,164],[60,13976,359],{"className":13977},[127,178,164],[60,13979,13981],{"className":13980},[183],[60,13982,13984,14004],{"className":13983},[139,140],[60,13985,13987,14001],{"className":13986},[144],[60,13988,13990],{"className":13989,"style":193},[148],[60,13991,13992,13995],{"style":2391},[60,13993],{"className":13994,"style":200},[156],[60,13996,13998],{"className":13997},[161,204,205,164],[60,13999,104],{"className":14000},[127,164],[60,14002,213],{"className":14003},[212],[60,14005,14007],{"className":14006},[144],[60,14008,14010],{"className":14009,"style":220},[148],[60,14011],{},[60,14013,14014,14017],{"style":225},[60,14015],{"className":14016,"style":157},[156],[60,14018],{"className":14019,"style":233},[232],[60,14021,14022,14025],{"style":236},[60,14023],{"className":14024,"style":157},[156],[60,14026,14028],{"className":14027},[161,162,163,164],[60,14029,14031,14034],{"className":14030},[127,164],[60,14032,87],{"className":14033,"style":171},[127,164],[60,14035,100],{"className":14036,"style":179},[127,178,164],[60,14038,213],{"className":14039},[212],[60,14041,14043],{"className":14042},[144],[60,14044,14046],{"className":14045,"style":2969},[148],[60,14047],{},[60,14049],{"className":14050},[267,132],"\n利用公式 (3.17)：\n",[60,14053,14055,14129],{"className":14054},[63],[60,14056,14058],{"className":14057},[67],[69,14059,14060],{"xmlns":71},[73,14061,14062,14126],{},[76,14063,14064,14082,14084,14086,14088,14090,14096,14098,14104,14106,14108],{},[79,14065,14066,14072],{},[76,14067,14068,14070],{},[84,14069,87],{"mathvariant":86},[84,14071,100],{},[76,14073,14074,14076],{},[84,14075,87],{"mathvariant":86},[96,14077,14078,14080],{},[84,14079,359],{},[102,14081,104],{},[397,14083,448],{},[397,14085,817],{},[84,14087,562],{},[397,14089,400],{"stretchy":399},[96,14091,14092,14094],{},[84,14093,359],{},[102,14095,104],{},[397,14097,569],{"separator":114},[96,14099,14100,14102],{},[84,14101,100],{},[102,14103,104],{},[397,14105,405],{"stretchy":399},[397,14107,2831],{},[79,14109,14110,14116],{},[76,14111,14112,14114],{},[84,14113,87],{"mathvariant":86},[84,14115,100],{},[76,14117,14118,14120],{},[84,14119,87],{"mathvariant":86},[96,14121,14122,14124],{},[84,14123,100],{},[102,14125,104],{},[106,14127,14128],{"encoding":108},"\\frac{\\partial y}{\\partial x_0} = -f(x_0, y_0) \\cdot \\frac{\\partial y}{\\partial y_0}",[60,14130,14132,14258,14371],{"className":14131,"ariaHidden":114},[113],[60,14133,14135,14138,14249,14252,14255],{"className":14134},[118],[60,14136],{"className":14137,"style":2862},[122],[60,14139,14141,14144,14246],{"className":14140},[127],[60,14142],{"className":14143},[131,132],[60,14145,14147],{"className":14146},[79],[60,14148,14150,14238],{"className":14149},[139,140],[60,14151,14153,14235],{"className":14152},[144],[60,14154,14156,14210,14218],{"className":14155,"style":149},[148],[60,14157,14158,14161],{"style":152},[60,14159],{"className":14160,"style":157},[156],[60,14162,14164],{"className":14163},[161,162,163,164],[60,14165,14167,14170],{"className":14166},[127,164],[60,14168,87],{"className":14169,"style":171},[127,164],[60,14171,14173,14176],{"className":14172},[127,164],[60,14174,359],{"className":14175},[127,178,164],[60,14177,14179],{"className":14178},[183],[60,14180,14182,14202],{"className":14181},[139,140],[60,14183,14185,14199],{"className":14184},[144],[60,14186,14188],{"className":14187,"style":193},[148],[60,14189,14190,14193],{"style":2391},[60,14191],{"className":14192,"style":200},[156],[60,14194,14196],{"className":14195},[161,204,205,164],[60,14197,104],{"className":14198},[127,164],[60,14200,213],{"className":14201},[212],[60,14203,14205],{"className":14204},[144],[60,14206,14208],{"className":14207,"style":220},[148],[60,14209],{},[60,14211,14212,14215],{"style":225},[60,14213],{"className":14214,"style":157},[156],[60,14216],{"className":14217,"style":233},[232],[60,14219,14220,14223],{"style":236},[60,14221],{"className":14222,"style":157},[156],[60,14224,14226],{"className":14225},[161,162,163,164],[60,14227,14229,14232],{"className":14228},[127,164],[60,14230,87],{"className":14231,"style":171},[127,164],[60,14233,100],{"className":14234,"style":179},[127,178,164],[60,14236,213],{"className":14237},[212],[60,14239,14241],{"className":14240},[144],[60,14242,14244],{"className":14243,"style":2969},[148],[60,14245],{},[60,14247],{"className":14248},[267,132],[60,14250],{"className":14251,"style":470},[469],[60,14253,448],{"className":14254},[474],[60,14256],{"className":14257,"style":470},[469],[60,14259,14261,14264,14267,14270,14273,14313,14316,14319,14359,14362,14365,14368],{"className":14260},[118],[60,14262],{"className":14263,"style":418},[122],[60,14265,817],{"className":14266},[127],[60,14268,562],{"className":14269,"style":639},[127,178],[60,14271,400],{"className":14272},[131],[60,14274,14276,14279],{"className":14275},[127],[60,14277,359],{"className":14278},[127,178],[60,14280,14282],{"className":14281},[183],[60,14283,14285,14305],{"className":14284},[139,140],[60,14286,14288,14302],{"className":14287},[144],[60,14289,14291],{"className":14290,"style":318},[148],[60,14292,14293,14296],{"style":1940},[60,14294],{"className":14295,"style":325},[156],[60,14297,14299],{"className":14298},[161,162,163,164],[60,14300,104],{"className":14301},[127,164],[60,14303,213],{"className":14304},[212],[60,14306,14308],{"className":14307},[144],[60,14309,14311],{"className":14310,"style":341},[148],[60,14312],{},[60,14314,569],{"className":14315},[649],[60,14317],{"className":14318,"style":653},[469],[60,14320,14322,14325],{"className":14321},[127],[60,14323,100],{"className":14324,"style":179},[127,178],[60,14326,14328],{"className":14327},[183],[60,14329,14331,14351],{"className":14330},[139,140],[60,14332,14334,14348],{"className":14333},[144],[60,14335,14337],{"className":14336,"style":318},[148],[60,14338,14339,14342],{"style":321},[60,14340],{"className":14341,"style":325},[156],[60,14343,14345],{"className":14344},[161,162,163,164],[60,14346,104],{"className":14347},[127,164],[60,14349,213],{"className":14350},[212],[60,14352,14354],{"className":14353},[144],[60,14355,14357],{"className":14356,"style":341},[148],[60,14358],{},[60,14360,405],{"className":14361},[267],[60,14363],{"className":14364,"style":924},[469],[60,14366,2831],{"className":14367},[928],[60,14369],{"className":14370,"style":924},[469],[60,14372,14374,14377],{"className":14373},[118],[60,14375],{"className":14376,"style":123},[122],[60,14378,14380,14383,14485],{"className":14379},[127],[60,14381],{"className":14382},[131,132],[60,14384,14386],{"className":14385},[79],[60,14387,14389,14477],{"className":14388},[139,140],[60,14390,14392,14474],{"className":14391},[144],[60,14393,14395,14449,14457],{"className":14394,"style":149},[148],[60,14396,14397,14400],{"style":152},[60,14398],{"className":14399,"style":157},[156],[60,14401,14403],{"className":14402},[161,162,163,164],[60,14404,14406,14409],{"className":14405},[127,164],[60,14407,87],{"className":14408,"style":171},[127,164],[60,14410,14412,14415],{"className":14411},[127,164],[60,14413,100],{"className":14414,"style":179},[127,178,164],[60,14416,14418],{"className":14417},[183],[60,14419,14421,14441],{"className":14420},[139,140],[60,14422,14424,14438],{"className":14423},[144],[60,14425,14427],{"className":14426,"style":193},[148],[60,14428,14429,14432],{"style":196},[60,14430],{"className":14431,"style":200},[156],[60,14433,14435],{"className":14434},[161,204,205,164],[60,14436,104],{"className":14437},[127,164],[60,14439,213],{"className":14440},[212],[60,14442,14444],{"className":14443},[144],[60,14445,14447],{"className":14446,"style":220},[148],[60,14448],{},[60,14450,14451,14454],{"style":225},[60,14452],{"className":14453,"style":157},[156],[60,14455],{"className":14456,"style":233},[232],[60,14458,14459,14462],{"style":236},[60,14460],{"className":14461,"style":157},[156],[60,14463,14465],{"className":14464},[161,162,163,164],[60,14466,14468,14471],{"className":14467},[127,164],[60,14469,87],{"className":14470,"style":171},[127,164],[60,14472,100],{"className":14473,"style":179},[127,178,164],[60,14475,213],{"className":14476},[212],[60,14478,14480],{"className":14479},[144],[60,14481,14483],{"className":14482,"style":261},[148],[60,14484],{},[60,14486],{"className":14487},[267,132],[60,14489,14491,14522],{"className":14490},[63],[60,14492,14494],{"className":14493},[67],[69,14495,14496],{"xmlns":71},[73,14497,14498,14520],{},[76,14499,14500,14502,14504,14510,14512,14518],{},[84,14501,562],{},[397,14503,400],{"stretchy":399},[96,14505,14506,14508],{},[84,14507,359],{},[102,14509,104],{},[397,14511,569],{"separator":114},[96,14513,14514,14516],{},[84,14515,100],{},[102,14517,104],{},[397,14519,405],{"stretchy":399},[106,14521,7188],{"encoding":108},[60,14523,14525],{"className":14524,"ariaHidden":114},[113],[60,14526,14528,14531,14534,14537,14577,14580,14583,14623],{"className":14527},[118],[60,14529],{"className":14530,"style":418},[122],[60,14532,562],{"className":14533,"style":639},[127,178],[60,14535,400],{"className":14536},[131],[60,14538,14540,14543],{"className":14539},[127],[60,14541,359],{"className":14542},[127,178],[60,14544,14546],{"className":14545},[183],[60,14547,14549,14569],{"className":14548},[139,140],[60,14550,14552,14566],{"className":14551},[144],[60,14553,14555],{"className":14554,"style":318},[148],[60,14556,14557,14560],{"style":1940},[60,14558],{"className":14559,"style":325},[156],[60,14561,14563],{"className":14562},[161,162,163,164],[60,14564,104],{"className":14565},[127,164],[60,14567,213],{"className":14568},[212],[60,14570,14572],{"className":14571},[144],[60,14573,14575],{"className":14574,"style":341},[148],[60,14576],{},[60,14578,569],{"className":14579},[649],[60,14581],{"className":14582,"style":653},[469],[60,14584,14586,14589],{"className":14585},[127],[60,14587,100],{"className":14588,"style":179},[127,178],[60,14590,14592],{"className":14591},[183],[60,14593,14595,14615],{"className":14594},[139,140],[60,14596,14598,14612],{"className":14597},[144],[60,14599,14601],{"className":14600,"style":318},[148],[60,14602,14603,14606],{"style":321},[60,14604],{"className":14605,"style":325},[156],[60,14607,14609],{"className":14608},[161,162,163,164],[60,14610,104],{"className":14611},[127,164],[60,14613,213],{"className":14614},[212],[60,14616,14618],{"className":14617},[144],[60,14619,14621],{"className":14620,"style":341},[148],[60,14622],{},[60,14624,405],{"className":14625},[267],"，也就是 ",[60,14628,14630,14654],{"className":14629},[63],[60,14631,14633],{"className":14632},[67],[69,14634,14635],{"xmlns":71},[73,14636,14637,14651],{},[76,14638,14639,14641,14643,14645,14647,14649],{},[84,14640,562],{},[397,14642,400],{"stretchy":399},[102,14644,820],{},[397,14646,569],{"separator":114},[102,14648,104],{},[397,14650,405],{"stretchy":399},[106,14652,14653],{"encoding":108},"f(1,0)",[60,14655,14657],{"className":14656,"ariaHidden":114},[113],[60,14658,14660,14663,14666,14669,14672,14675,14678,14681],{"className":14659},[118],[60,14661],{"className":14662,"style":418},[122],[60,14664,562],{"className":14665,"style":639},[127,178],[60,14667,400],{"className":14668},[131],[60,14670,820],{"className":14671},[127],[60,14673,569],{"className":14674},[649],[60,14676],{"className":14677,"style":653},[469],[60,14679,104],{"className":14680},[127],[60,14682,405],{"className":14683},[267],[60,14685,14687,14733],{"className":14686},[63],[60,14688,14690],{"className":14689},[67],[69,14691,14692],{"xmlns":71},[73,14693,14694,14730],{},[76,14695,14696,14698,14700,14702,14704,14706,14708,14710,14712,14714,14726,14728],{},[84,14697,562],{},[397,14699,400],{"stretchy":399},[102,14701,820],{},[397,14703,569],{"separator":114},[102,14705,104],{},[397,14707,405],{"stretchy":399},[397,14709,448],{},[84,14711,9061],{},[397,14713,1465],{},[76,14715,14716,14718,14724],{},[397,14717,400],{"fence":114},[79,14719,14720,14722],{},[102,14721,104],{},[102,14723,820],{},[397,14725,405],{"fence":114},[397,14727,448],{},[102,14729,104],{},[106,14731,14732],{"encoding":108},"f(1,0) = \\sin\\left(\\frac{0}{1}\\right) = 0",[60,14734,14736,14772,14876],{"className":14735,"ariaHidden":114},[113],[60,14737,14739,14742,14745,14748,14751,14754,14757,14760,14763,14766,14769],{"className":14738},[118],[60,14740],{"className":14741,"style":418},[122],[60,14743,562],{"className":14744,"style":639},[127,178],[60,14746,400],{"className":14747},[131],[60,14749,820],{"className":14750},[127],[60,14752,569],{"className":14753},[649],[60,14755],{"className":14756,"style":653},[469],[60,14758,104],{"className":14759},[127],[60,14761,405],{"className":14762},[267],[60,14764],{"className":14765,"style":470},[469],[60,14767,448],{"className":14768},[474],[60,14770],{"className":14771,"style":470},[469],[60,14773,14775,14778,14781,14784,14867,14870,14873],{"className":14774},[118],[60,14776],{"className":14777,"style":11252},[122],[60,14779,9061],{"className":14780},[1495],[60,14782],{"className":14783,"style":653},[469],[60,14785,14787,14793,14861],{"className":14786},[2326],[60,14788,14790],{"className":14789,"style":2331},[131,2330],[60,14791,400],{"className":14792},[2335,205],[60,14794,14796,14799,14858],{"className":14795},[127],[60,14797],{"className":14798},[131,132],[60,14800,14802],{"className":14801},[79],[60,14803,14805,14850],{"className":14804},[139,140],[60,14806,14808,14847],{"className":14807},[144],[60,14809,14811,14825,14833],{"className":14810,"style":11547},[148],[60,14812,14813,14816],{"style":152},[60,14814],{"className":14815,"style":157},[156],[60,14817,14819],{"className":14818},[161,162,163,164],[60,14820,14822],{"className":14821},[127,164],[60,14823,820],{"className":14824},[127,164],[60,14826,14827,14830],{"style":225},[60,14828],{"className":14829,"style":157},[156],[60,14831],{"className":14832,"style":233},[232],[60,14834,14835,14838],{"style":1105},[60,14836],{"className":14837,"style":157},[156],[60,14839,14841],{"className":14840},[161,162,163,164],[60,14842,14844],{"className":14843},[127,164],[60,14845,104],{"className":14846},[127,164],[60,14848,213],{"className":14849},[212],[60,14851,14853],{"className":14852},[144],[60,14854,14856],{"className":14855,"style":3907},[148],[60,14857],{},[60,14859],{"className":14860},[267,132],[60,14862,14864],{"className":14863,"style":2331},[267,2330],[60,14865,405],{"className":14866},[2335,205],[60,14868],{"className":14869,"style":470},[469],[60,14871,448],{"className":14872},[474],[60,14874],{"className":14875,"style":470},[469],[60,14877,14879,14882],{"className":14878},[118],[60,14880],{"className":14881,"style":484},[122],[60,14883,104],{"className":14884},[127],"\n由于前面的系数是 0，无论后面是多少，结果都是 0。\n",[60,14887,14889,14933],{"className":14888},[63],[60,14890,14892],{"className":14891},[67],[69,14893,14894],{"xmlns":71},[73,14895,14896,14930],{},[76,14897,14898,14916,14918,14920,14922,14924,14926,14928],{},[79,14899,14900,14906],{},[76,14901,14902,14904],{},[84,14903,87],{"mathvariant":86},[84,14905,100],{},[76,14907,14908,14910],{},[84,14909,87],{"mathvariant":86},[96,14911,14912,14914],{},[84,14913,359],{},[102,14915,104],{},[397,14917,448],{},[397,14919,817],{},[102,14921,104],{},[397,14923,2831],{},[84,14925,359],{},[397,14927,448],{},[102,14929,104],{},[106,14931,14932],{"encoding":108},"\\frac{\\partial y}{\\partial x_0} = -0 \\cdot x = 0",[60,14934,14936,15062,15083,15101],{"className":14935,"ariaHidden":114},[113],[60,14937,14939,14942,15053,15056,15059],{"className":14938},[118],[60,14940],{"className":14941,"style":2862},[122],[60,14943,14945,14948,15050],{"className":14944},[127],[60,14946],{"className":14947},[131,132],[60,14949,14951],{"className":14950},[79],[60,14952,14954,15042],{"className":14953},[139,140],[60,14955,14957,15039],{"className":14956},[144],[60,14958,14960,15014,15022],{"className":14959,"style":149},[148],[60,14961,14962,14965],{"style":152},[60,14963],{"className":14964,"style":157},[156],[60,14966,14968],{"className":14967},[161,162,163,164],[60,14969,14971,14974],{"className":14970},[127,164],[60,14972,87],{"className":14973,"style":171},[127,164],[60,14975,14977,14980],{"className":14976},[127,164],[60,14978,359],{"className":14979},[127,178,164],[60,14981,14983],{"className":14982},[183],[60,14984,14986,15006],{"className":14985},[139,140],[60,14987,14989,15003],{"className":14988},[144],[60,14990,14992],{"className":14991,"style":193},[148],[60,14993,14994,14997],{"style":2391},[60,14995],{"className":14996,"style":200},[156],[60,14998,15000],{"className":14999},[161,204,205,164],[60,15001,104],{"className":15002},[127,164],[60,15004,213],{"className":15005},[212],[60,15007,15009],{"className":15008},[144],[60,15010,15012],{"className":15011,"style":220},[148],[60,15013],{},[60,15015,15016,15019],{"style":225},[60,15017],{"className":15018,"style":157},[156],[60,15020],{"className":15021,"style":233},[232],[60,15023,15024,15027],{"style":236},[60,15025],{"className":15026,"style":157},[156],[60,15028,15030],{"className":15029},[161,162,163,164],[60,15031,15033,15036],{"className":15032},[127,164],[60,15034,87],{"className":15035,"style":171},[127,164],[60,15037,100],{"className":15038,"style":179},[127,178,164],[60,15040,213],{"className":15041},[212],[60,15043,15045],{"className":15044},[144],[60,15046,15048],{"className":15047,"style":2969},[148],[60,15049],{},[60,15051],{"className":15052},[267,132],[60,15054],{"className":15055,"style":470},[469],[60,15057,448],{"className":15058},[474],[60,15060],{"className":15061,"style":470},[469],[60,15063,15065,15068,15071,15074,15077,15080],{"className":15064},[118],[60,15066],{"className":15067,"style":1197},[122],[60,15069,817],{"className":15070},[127],[60,15072,104],{"className":15073},[127],[60,15075],{"className":15076,"style":924},[469],[60,15078,2831],{"className":15079},[928],[60,15081],{"className":15082,"style":924},[469],[60,15084,15086,15089,15092,15095,15098],{"className":15085},[118],[60,15087],{"className":15088,"style":371},[122],[60,15090,359],{"className":15091},[127,178],[60,15093],{"className":15094,"style":470},[469],[60,15096,448],{"className":15097},[474],[60,15099],{"className":15100,"style":470},[469],[60,15102,15104,15107],{"className":15103},[118],[60,15105],{"className":15106,"style":484},[122],[60,15108,104],{"className":15109},[127],[26,15111,13723],{},[60,15113,15115,15149],{"className":15114},[63],[60,15116,15118],{"className":15117},[67],[69,15119,15120],{"xmlns":71},[73,15121,15122,15146],{},[76,15123,15124,15142,15144],{},[79,15125,15126,15132],{},[76,15127,15128,15130],{},[84,15129,87],{"mathvariant":6025},[84,15131,100],{"mathvariant":6025},[76,15133,15134,15136],{},[84,15135,87],{"mathvariant":6025},[96,15137,15138,15140],{},[84,15139,359],{"mathvariant":6025},[102,15141,104],{"mathvariant":6025},[397,15143,448],{},[102,15145,104],{"mathvariant":6025},[106,15147,15148],{"encoding":108},"\\mathbf{\\frac{\\partial y}{\\partial x_0} = 0}",[60,15150,15152],{"className":15151,"ariaHidden":114},[113],[60,15153,15155,15158],{"className":15154},[118],[60,15156],{"className":15157,"style":2862},[122],[60,15159,15161,15269,15272,15275,15278],{"className":15160},[127],[60,15162,15164,15167,15266],{"className":15163},[127],[60,15165],{"className":15166},[131,132],[60,15168,15170],{"className":15169},[79],[60,15171,15173,15258],{"className":15172},[139,140],[60,15174,15176,15255],{"className":15175},[144],[60,15177,15179,15233,15241],{"className":15178,"style":149},[148],[60,15180,15181,15184],{"style":152},[60,15182],{"className":15183,"style":157},[156],[60,15185,15187],{"className":15186},[161,162,163,164],[60,15188,15190,15193],{"className":15189},[127,164],[60,15191,87],{"className":15192,"style":6122},[127,6121,164],[60,15194,15196,15199],{"className":15195},[127,164],[60,15197,359],{"className":15198},[127,6121,164],[60,15200,15202],{"className":15201},[183],[60,15203,15205,15225],{"className":15204},[139,140],[60,15206,15208,15222],{"className":15207},[144],[60,15209,15211],{"className":15210,"style":193},[148],[60,15212,15213,15216],{"style":2391},[60,15214],{"className":15215,"style":200},[156],[60,15217,15219],{"className":15218},[161,204,205,164],[60,15220,104],{"className":15221},[127,6121,164],[60,15223,213],{"className":15224},[212],[60,15226,15228],{"className":15227},[144],[60,15229,15231],{"className":15230,"style":220},[148],[60,15232],{},[60,15234,15235,15238],{"style":225},[60,15236],{"className":15237,"style":157},[156],[60,15239],{"className":15240,"style":233},[232],[60,15242,15243,15246],{"style":236},[60,15244],{"className":15245,"style":157},[156],[60,15247,15249],{"className":15248},[161,162,163,164],[60,15250,15252],{"className":15251},[127,164],[60,15253,13868],{"className":15254,"style":6129},[127,6121,164],[60,15256,213],{"className":15257},[212],[60,15259,15261],{"className":15260},[144],[60,15262,15264],{"className":15263,"style":2969},[148],[60,15265],{},[60,15267],{"className":15268},[267,132],[60,15270],{"className":15271,"style":470},[469],[60,15273,448],{"className":15274},[474],[60,15276],{"className":15277,"style":470},[469],[60,15279,104],{"className":15280},[127,6121],[15,15282],{},[18,15284,15285],{"id":15285},"总结与建议",[30,15287,15288,15510],{},[33,15289,15290,15293,15294,15446,15447,15509],{},[26,15291,15292],{},"理论核心："," 只要记住，解对初值的偏导数 ",[60,15295,15297,15326],{"className":15296},[63],[60,15298,15300],{"className":15299},[67],[69,15301,15302],{"xmlns":71},[73,15303,15304,15324],{},[76,15305,15306],{},[79,15307,15308,15314],{},[76,15309,15310,15312],{},[84,15311,87],{"mathvariant":86},[84,15313,90],{},[76,15315,15316,15318],{},[84,15317,87],{"mathvariant":86},[96,15319,15320,15322],{},[84,15321,100],{},[102,15323,104],{},[106,15325,109],{"encoding":108},[60,15327,15329],{"className":15328,"ariaHidden":114},[113],[60,15330,15332,15335],{"className":15331},[118],[60,15333],{"className":15334,"style":123},[122],[60,15336,15338,15341,15443],{"className":15337},[127],[60,15339],{"className":15340},[131,132],[60,15342,15344],{"className":15343},[79],[60,15345,15347,15435],{"className":15346},[139,140],[60,15348,15350,15432],{"className":15349},[144],[60,15351,15353,15407,15415],{"className":15352,"style":149},[148],[60,15354,15355,15358],{"style":152},[60,15356],{"className":15357,"style":157},[156],[60,15359,15361],{"className":15360},[161,162,163,164],[60,15362,15364,15367],{"className":15363},[127,164],[60,15365,87],{"className":15366,"style":171},[127,164],[60,15368,15370,15373],{"className":15369},[127,164],[60,15371,100],{"className":15372,"style":179},[127,178,164],[60,15374,15376],{"className":15375},[183],[60,15377,15379,15399],{"className":15378},[139,140],[60,15380,15382,15396],{"className":15381},[144],[60,15383,15385],{"className":15384,"style":193},[148],[60,15386,15387,15390],{"style":196},[60,15388],{"className":15389,"style":200},[156],[60,15391,15393],{"className":15392},[161,204,205,164],[60,15394,104],{"className":15395},[127,164],[60,15397,213],{"className":15398},[212],[60,15400,15402],{"className":15401},[144],[60,15403,15405],{"className":15404,"style":220},[148],[60,15406],{},[60,15408,15409,15412],{"style":225},[60,15410],{"className":15411,"style":157},[156],[60,15413],{"className":15414,"style":233},[232],[60,15416,15417,15420],{"style":236},[60,15418],{"className":15419,"style":157},[156],[60,15421,15423],{"className":15422},[161,162,163,164],[60,15424,15426,15429],{"className":15425},[127,164],[60,15427,87],{"className":15428,"style":171},[127,164],[60,15430,90],{"className":15431},[127,178,164],[60,15433,213],{"className":15434},[212],[60,15436,15438],{"className":15437},[144],[60,15439,15441],{"className":15440,"style":261},[148],[60,15442],{},[60,15444],{"className":15445},[267,132]," 本质上是一个解的“变分”，它服从一个线性的微分关系，所以结果总是一个指数积分形式 (",[60,15448,15450,15478],{"className":15449},[63],[60,15451,15453],{"className":15452},[67],[69,15454,15455],{"xmlns":71},[73,15456,15457,15475],{},[76,15458,15459,15461,15463,15465,15467,15470,15473],{},[84,15460,2119],{},[397,15462,1465],{},[397,15464,400],{"stretchy":399},[397,15466,2131],{},[397,15468,15469],{},"…",[13095,15471,15472],{}," ",[397,15474,405],{"stretchy":399},[106,15476,15477],{"encoding":108},"\\exp(\\int \\dots)",[60,15479,15481],{"className":15480,"ariaHidden":114},[113],[60,15482,15484,15488,15491,15494,15497,15500,15503,15506],{"className":15483},[118],[60,15485],{"className":15486,"style":15487},[122],"height:1.1111em;vertical-align:-0.3061em;",[60,15489,2119],{"className":15490},[1495],[60,15492,400],{"className":15493},[131],[60,15495,2131],{"className":15496,"style":2345},[1495,2343,2344],[60,15498],{"className":15499,"style":653},[469],[60,15501,15469],{"className":15502},[2326],[60,15504],{"className":15505,"style":653},[469],[60,15507,405],{"className":15508},[267],")。",[33,15511,15512,15515],{},[26,15513,15514],{},"做题技巧：",[51,15516,15517,15564],{},[33,15518,15519,15520,15563],{},"如果是线性方程（如题1），直接代入 ",[60,15521,15523,15542],{"className":15522},[63],[60,15524,15526],{"className":15525},[67],[69,15527,15528],{"xmlns":71},[73,15529,15530,15540],{},[76,15531,15532,15534,15536,15538],{},[84,15533,3539],{},[397,15535,400],{"stretchy":399},[84,15537,359],{},[397,15539,405],{"stretchy":399},[106,15541,6429],{"encoding":108},[60,15543,15545],{"className":15544,"ariaHidden":114},[113],[60,15546,15548,15551,15554,15557,15560],{"className":15547},[118],[60,15549],{"className":15550,"style":418},[122],[60,15552,3539],{"className":15553,"style":3572},[127,178],[60,15555,400],{"className":15556},[131],[60,15558,359],{"className":15559},[127,178],[60,15561,405],{"className":15562},[267]," 即可。",[33,15565,15566,15567,15570,15571,15682,15683,15711],{},"如果是非线性方程（如题2），",[26,15568,15569],{},"必须先找出原方程的特解","，代入 ",[60,15572,15574,15599],{"className":15573},[63],[60,15575,15577],{"className":15576},[67],[69,15578,15579],{"xmlns":71},[73,15580,15581,15597],{},[76,15582,15583],{},[79,15584,15585,15591],{},[76,15586,15587,15589],{},[84,15588,87],{"mathvariant":86},[84,15590,562],{},[76,15592,15593,15595],{},[84,15594,87],{"mathvariant":86},[84,15596,100],{},[106,15598,2585],{"encoding":108},[60,15600,15602],{"className":15601,"ariaHidden":114},[113],[60,15603,15605,15608],{"className":15604},[118],[60,15606],{"className":15607,"style":123},[122],[60,15609,15611,15614,15679],{"className":15610},[127],[60,15612],{"className":15613},[131,132],[60,15615,15617],{"className":15616},[79],[60,15618,15620,15671],{"className":15619},[139,140],[60,15621,15623,15668],{"className":15622},[144],[60,15624,15626,15643,15651],{"className":15625,"style":149},[148],[60,15627,15628,15631],{"style":152},[60,15629],{"className":15630,"style":157},[156],[60,15632,15634],{"className":15633},[161,162,163,164],[60,15635,15637,15640],{"className":15636},[127,164],[60,15638,87],{"className":15639,"style":171},[127,164],[60,15641,100],{"className":15642,"style":179},[127,178,164],[60,15644,15645,15648],{"style":225},[60,15646],{"className":15647,"style":157},[156],[60,15649],{"className":15650,"style":233},[232],[60,15652,15653,15656],{"style":236},[60,15654],{"className":15655,"style":157},[156],[60,15657,15659],{"className":15658},[161,162,163,164],[60,15660,15662,15665],{"className":15661},[127,164],[60,15663,87],{"className":15664,"style":171},[127,164],[60,15666,562],{"className":15667,"style":639},[127,178,164],[60,15669,213],{"className":15670},[212],[60,15672,15674],{"className":15673},[144],[60,15675,15677],{"className":15676,"style":261},[148],[60,15678],{},[60,15680],{"className":15681},[267,132]," 把它变成只含 ",[60,15684,15686,15699],{"className":15685},[63],[60,15687,15689],{"className":15688},[67],[69,15690,15691],{"xmlns":71},[73,15692,15693,15697],{},[76,15694,15695],{},[84,15696,359],{},[106,15698,359],{"encoding":108},[60,15700,15702],{"className":15701,"ariaHidden":114},[113],[60,15703,15705,15708],{"className":15704},[118],[60,15706],{"className":15707,"style":371},[122],[60,15709,359],{"className":15710},[127,178]," 的函数，才能进行积分。",[23,15713,15714,15715,15718],{},"这些题目覆盖了",[26,15716,15717],{},"线性微分方程的四大支柱","：",[30,15720,15721,15727,15733,15739],{},[33,15722,15723,15726],{},[26,15724,15725],{},"叠加原理","（解的性质）",[33,15728,15729,15732],{},[26,15730,15731],{},"常数变易法","（解的计算，核心中的核心）",[33,15734,15735,15738],{},[26,15736,15737],{},"初值问题","（归一化）",[33,15740,15741,15744],{},[26,15742,15743],{},"理论证明","（朗斯基行列式与解的空间结构）",[15,15746],{},[18,15748,15750],{"id":15749},"_2-证明非齐次线性微分方程的叠加原理","2. 证明非齐次线性微分方程的叠加原理",[23,15752,15753,15756,15757,15827,15828,15899,15900,15827,15970,16040,16041,16175,16176,488],{},[26,15754,15755],{},"核心思想：","\n微分方程其实是一个“机器”（算子）。你把函数放进去，它就吐出一个结果。\n这道题是说：如果把 ",[60,15758,15760,15778],{"className":15759},[63],[60,15761,15763],{"className":15762},[67],[69,15764,15765],{"xmlns":71},[73,15766,15767,15775],{},[76,15768,15769],{},[96,15770,15771,15773],{},[84,15772,359],{},[102,15774,820],{},[106,15776,15777],{"encoding":108},"x_1",[60,15779,15781],{"className":15780,"ariaHidden":114},[113],[60,15782,15784,15787],{"className":15783},[118],[60,15785],{"className":15786,"style":2734},[122],[60,15788,15790,15793],{"className":15789},[127],[60,15791,359],{"className":15792},[127,178],[60,15794,15796],{"className":15795},[183],[60,15797,15799,15819],{"className":15798},[139,140],[60,15800,15802,15816],{"className":15801},[144],[60,15803,15805],{"className":15804,"style":318},[148],[60,15806,15807,15810],{"style":1940},[60,15808],{"className":15809,"style":325},[156],[60,15811,15813],{"className":15812},[161,162,163,164],[60,15814,820],{"className":15815},[127,164],[60,15817,213],{"className":15818},[212],[60,15820,15822],{"className":15821},[144],[60,15823,15825],{"className":15824,"style":341},[148],[60,15826],{}," 放进去得到 ",[60,15829,15831,15849],{"className":15830},[63],[60,15832,15834],{"className":15833},[67],[69,15835,15836],{"xmlns":71},[73,15837,15838,15846],{},[76,15839,15840],{},[96,15841,15842,15844],{},[84,15843,562],{},[102,15845,820],{},[106,15847,15848],{"encoding":108},"f_1",[60,15850,15852],{"className":15851,"ariaHidden":114},[113],[60,15853,15855,15858],{"className":15854},[118],[60,15856],{"className":15857,"style":694},[122],[60,15859,15861,15864],{"className":15860},[127],[60,15862,562],{"className":15863,"style":639},[127,178],[60,15865,15867],{"className":15866},[183],[60,15868,15870,15891],{"className":15869},[139,140],[60,15871,15873,15888],{"className":15872},[144],[60,15874,15876],{"className":15875,"style":318},[148],[60,15877,15879,15882],{"style":15878},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[60,15880],{"className":15881,"style":325},[156],[60,15883,15885],{"className":15884},[161,162,163,164],[60,15886,820],{"className":15887},[127,164],[60,15889,213],{"className":15890},[212],[60,15892,15894],{"className":15893},[144],[60,15895,15897],{"className":15896,"style":341},[148],[60,15898],{},"，把 ",[60,15901,15903,15921],{"className":15902},[63],[60,15904,15906],{"className":15905},[67],[69,15907,15908],{"xmlns":71},[73,15909,15910,15918],{},[76,15911,15912],{},[96,15913,15914,15916],{},[84,15915,359],{},[102,15917,814],{},[106,15919,15920],{"encoding":108},"x_2",[60,15922,15924],{"className":15923,"ariaHidden":114},[113],[60,15925,15927,15930],{"className":15926},[118],[60,15928],{"className":15929,"style":2734},[122],[60,15931,15933,15936],{"className":15932},[127],[60,15934,359],{"className":15935},[127,178],[60,15937,15939],{"className":15938},[183],[60,15940,15942,15962],{"className":15941},[139,140],[60,15943,15945,15959],{"className":15944},[144],[60,15946,15948],{"className":15947,"style":318},[148],[60,15949,15950,15953],{"style":1940},[60,15951],{"className":15952,"style":325},[156],[60,15954,15956],{"className":15955},[161,162,163,164],[60,15957,814],{"className":15958},[127,164],[60,15960,213],{"className":15961},[212],[60,15963,15965],{"className":15964},[144],[60,15966,15968],{"className":15967,"style":341},[148],[60,15969],{},[60,15971,15973,15991],{"className":15972},[63],[60,15974,15976],{"className":15975},[67],[69,15977,15978],{"xmlns":71},[73,15979,15980,15988],{},[76,15981,15982],{},[96,15983,15984,15986],{},[84,15985,562],{},[102,15987,814],{},[106,15989,15990],{"encoding":108},"f_2",[60,15992,15994],{"className":15993,"ariaHidden":114},[113],[60,15995,15997,16000],{"className":15996},[118],[60,15998],{"className":15999,"style":694},[122],[60,16001,16003,16006],{"className":16002},[127],[60,16004,562],{"className":16005,"style":639},[127,178],[60,16007,16009],{"className":16008},[183],[60,16010,16012,16032],{"className":16011},[139,140],[60,16013,16015,16029],{"className":16014},[144],[60,16016,16018],{"className":16017,"style":318},[148],[60,16019,16020,16023],{"style":15878},[60,16021],{"className":16022,"style":325},[156],[60,16024,16026],{"className":16025},[161,162,163,164],[60,16027,814],{"className":16028},[127,164],[60,16030,213],{"className":16031},[212],[60,16033,16035],{"className":16034},[144],[60,16036,16038],{"className":16037,"style":341},[148],[60,16039],{},"，那么把 ",[60,16042,16044,16070],{"className":16043},[63],[60,16045,16047],{"className":16046},[67],[69,16048,16049],{"xmlns":71},[73,16050,16051,16067],{},[76,16052,16053,16059,16061],{},[96,16054,16055,16057],{},[84,16056,359],{},[102,16058,820],{},[397,16060,990],{},[96,16062,16063,16065],{},[84,16064,359],{},[102,16066,814],{},[106,16068,16069],{"encoding":108},"x_1+x_2",[60,16071,16073,16129],{"className":16072,"ariaHidden":114},[113],[60,16074,16076,16080,16120,16123,16126],{"className":16075},[118],[60,16077],{"className":16078,"style":16079},[122],"height:0.7333em;vertical-align:-0.15em;",[60,16081,16083,16086],{"className":16082},[127],[60,16084,359],{"className":16085},[127,178],[60,16087,16089],{"className":16088},[183],[60,16090,16092,16112],{"className":16091},[139,140],[60,16093,16095,16109],{"className":16094},[144],[60,16096,16098],{"className":16097,"style":318},[148],[60,16099,16100,16103],{"style":1940},[60,16101],{"className":16102,"style":325},[156],[60,16104,16106],{"className":16105},[161,162,163,164],[60,16107,820],{"className":16108},[127,164],[60,16110,213],{"className":16111},[212],[60,16113,16115],{"className":16114},[144],[60,16116,16118],{"className":16117,"style":341},[148],[60,16119],{},[60,16121],{"className":16122,"style":924},[469],[60,16124,990],{"className":16125},[928],[60,16127],{"className":16128,"style":924},[469],[60,16130,16132,16135],{"className":16131},[118],[60,16133],{"className":16134,"style":2734},[122],[60,16136,16138,16141],{"className":16137},[127],[60,16139,359],{"className":16140},[127,178],[60,16142,16144],{"className":16143},[183],[60,16145,16147,16167],{"className":16146},[139,140],[60,16148,16150,16164],{"className":16149},[144],[60,16151,16153],{"className":16152,"style":318},[148],[60,16154,16155,16158],{"style":1940},[60,16156],{"className":16157,"style":325},[156],[60,16159,16161],{"className":16160},[161,162,163,164],[60,16162,814],{"className":16163},[127,164],[60,16165,213],{"className":16166},[212],[60,16168,16170],{"className":16169},[144],[60,16171,16173],{"className":16172,"style":341},[148],[60,16174],{}," 一起放进去，得到的就是 ",[60,16177,16179,16205],{"className":16178},[63],[60,16180,16182],{"className":16181},[67],[69,16183,16184],{"xmlns":71},[73,16185,16186,16202],{},[76,16187,16188,16194,16196],{},[96,16189,16190,16192],{},[84,16191,562],{},[102,16193,820],{},[397,16195,990],{},[96,16197,16198,16200],{},[84,16199,562],{},[102,16201,814],{},[106,16203,16204],{"encoding":108},"f_1+f_2",[60,16206,16208,16263],{"className":16207,"ariaHidden":114},[113],[60,16209,16211,16214,16254,16257,16260],{"className":16210},[118],[60,16212],{"className":16213,"style":694},[122],[60,16215,16217,16220],{"className":16216},[127],[60,16218,562],{"className":16219,"style":639},[127,178],[60,16221,16223],{"className":16222},[183],[60,16224,16226,16246],{"className":16225},[139,140],[60,16227,16229,16243],{"className":16228},[144],[60,16230,16232],{"className":16231,"style":318},[148],[60,16233,16234,16237],{"style":15878},[60,16235],{"className":16236,"style":325},[156],[60,16238,16240],{"className":16239},[161,162,163,164],[60,16241,820],{"className":16242},[127,164],[60,16244,213],{"className":16245},[212],[60,16247,16249],{"className":16248},[144],[60,16250,16252],{"className":16251,"style":341},[148],[60,16253],{},[60,16255],{"className":16256,"style":924},[469],[60,16258,990],{"className":16259},[928],[60,16261],{"className":16262,"style":924},[469],[60,16264,16266,16269],{"className":16265},[118],[60,16267],{"className":16268,"style":694},[122],[60,16270,16272,16275],{"className":16271},[127],[60,16273,562],{"className":16274,"style":639},[127,178],[60,16276,16278],{"className":16277},[183],[60,16279,16281,16301],{"className":16280},[139,140],[60,16282,16284,16298],{"className":16283},[144],[60,16285,16287],{"className":16286,"style":318},[148],[60,16288,16289,16292],{"style":15878},[60,16290],{"className":16291,"style":325},[156],[60,16293,16295],{"className":16294},[161,162,163,164],[60,16296,814],{"className":16297},[127,164],[60,16299,213],{"className":16300},[212],[60,16302,16304],{"className":16303},[144],[60,16305,16307],{"className":16306,"style":341},[148],[60,16308],{},[23,16310,16311],{},[26,16312,16313],{},"证明步骤：",[23,16315,16316,16319,16320,16518,16519,16564,16565,16593,16594],{},[26,16317,16318],{},"第一步：简化符号（为了不晕车）","\n为了不每次都写那一长串 ",[60,16321,16323,16363],{"className":16322},[63],[60,16324,16326],{"className":16325},[67],[69,16327,16328],{"xmlns":71},[73,16329,16330,16360],{},[76,16331,16332,16355,16357],{},[79,16333,16334,16345],{},[76,16335,16336,16343],{},[550,16337,16338,16340],{},[84,16339,2173],{"mathvariant":86},[84,16341,16342],{},"n",[84,16344,359],{},[76,16346,16347,16349],{},[84,16348,2173],{"mathvariant":86},[550,16350,16351,16353],{},[84,16352,2152],{},[84,16354,16342],{},[397,16356,990],{},[397,16358,16359],{},"⋯",[106,16361,16362],{"encoding":108},"\\frac{\\mathrm{d}^n x}{\\mathrm{d}t^n} + \\cdots",[60,16364,16366,16508],{"className":16365,"ariaHidden":114},[113],[60,16367,16369,16373,16499,16502,16505],{"className":16368},[118],[60,16370],{"className":16371,"style":16372},[122],"height:1.256em;vertical-align:-0.345em;",[60,16374,16376,16379,16496],{"className":16375},[127],[60,16377],{"className":16378},[131,132],[60,16380,16382],{"className":16381},[79],[60,16383,16385,16488],{"className":16384},[139,140],[60,16386,16388,16485],{"className":16387},[144],[60,16389,16391,16434,16442],{"className":16390,"style":1046},[148],[60,16392,16393,16396],{"style":152},[60,16394],{"className":16395,"style":157},[156],[60,16397,16399],{"className":16398},[161,162,163,164],[60,16400,16402,16405],{"className":16401},[127,164],[60,16403,2173],{"className":16404},[127,3869,164],[60,16406,16408,16411],{"className":16407},[127,164],[60,16409,2152],{"className":16410},[127,178,164],[60,16412,16414],{"className":16413},[183],[60,16415,16417],{"className":16416},[139],[60,16418,16420],{"className":16419},[144],[60,16421,16423],{"className":16422,"style":1082},[148],[60,16424,16425,16428],{"style":1085},[60,16426],{"className":16427,"style":200},[156],[60,16429,16431],{"className":16430},[161,204,205,164],[60,16432,16342],{"className":16433},[127,178,164],[60,16435,16436,16439],{"style":225},[60,16437],{"className":16438,"style":157},[156],[60,16440],{"className":16441,"style":233},[232],[60,16443,16444,16447],{"style":1105},[60,16445],{"className":16446,"style":157},[156],[60,16448,16450],{"className":16449},[161,162,163,164],[60,16451,16453,16482],{"className":16452},[127,164],[60,16454,16456,16459],{"className":16455},[127,164],[60,16457,2173],{"className":16458},[127,3869,164],[60,16460,16462],{"className":16461},[183],[60,16463,16465],{"className":16464},[139],[60,16466,16468],{"className":16467},[144],[60,16469,16471],{"className":16470,"style":1139},[148],[60,16472,16473,16476],{"style":1142},[60,16474],{"className":16475,"style":200},[156],[60,16477,16479],{"className":16478},[161,204,205,164],[60,16480,16342],{"className":16481},[127,178,164],[60,16483,359],{"className":16484},[127,178,164],[60,16486,213],{"className":16487},[212],[60,16489,16491],{"className":16490},[144],[60,16492,16494],{"className":16493,"style":3907},[148],[60,16495],{},[60,16497],{"className":16498},[267,132],[60,16500],{"className":16501,"style":924},[469],[60,16503,990],{"className":16504},[928],[60,16506],{"className":16507,"style":924},[469],[60,16509,16511,16515],{"className":16510},[118],[60,16512],{"className":16513,"style":16514},[122],"height:0.313em;",[60,16516,16359],{"className":16517},[2326],"，我们定义一个记号 ",[60,16520,16522,16543],{"className":16521},[63],[60,16523,16525],{"className":16524},[67],[69,16526,16527],{"xmlns":71},[73,16528,16529,16540],{},[76,16530,16531,16534,16536,16538],{},[84,16532,16533],{},"L",[397,16535,4981],{"stretchy":399},[84,16537,359],{},[397,16539,5004],{"stretchy":399},[106,16541,16542],{"encoding":108},"L[x]",[60,16544,16546],{"className":16545,"ariaHidden":114},[113],[60,16547,16549,16552,16555,16558,16561],{"className":16548},[118],[60,16550],{"className":16551,"style":418},[122],[60,16553,16533],{"className":16554},[127,178],[60,16556,4981],{"className":16557},[131],[60,16559,359],{"className":16560},[127,178],[60,16562,5004],{"className":16563},[267],"。\n令 ",[60,16566,16568,16581],{"className":16567},[63],[60,16569,16571],{"className":16570},[67],[69,16572,16573],{"xmlns":71},[73,16574,16575,16579],{},[76,16576,16577],{},[84,16578,16533],{},[106,16580,16533],{"encoding":108},[60,16582,16584],{"className":16583,"ariaHidden":114},[113],[60,16585,16587,16590],{"className":16586},[118],[60,16588],{"className":16589,"style":532},[122],[60,16591,16533],{"className":16592},[127,178]," 代表方程左边的运算：\n",[60,16595,16597,16710],{"className":16596},[63],[60,16598,16600],{"className":16599},[67],[69,16601,16602],{"xmlns":71},[73,16603,16604,16707],{},[76,16605,16606,16608,16610,16612,16614,16616,16638,16640,16647,16649,16651,16653,16687,16689,16691,16693,16699,16701,16703,16705],{},[84,16607,16533],{},[397,16609,4981],{"stretchy":399},[84,16611,359],{},[397,16613,5004],{"stretchy":399},[397,16615,448],{},[79,16617,16618,16628],{},[76,16619,16620,16626],{},[550,16621,16622,16624],{},[84,16623,2173],{"mathvariant":86},[84,16625,16342],{},[84,16627,359],{},[76,16629,16630,16632],{},[84,16631,2173],{"mathvariant":86},[550,16633,16634,16636],{},[84,16635,2152],{},[84,16637,16342],{},[397,16639,990],{},[96,16641,16642,16645],{},[84,16643,16644],{},"a",[102,16646,820],{},[397,16648,400],{"stretchy":399},[84,16650,2152],{},[397,16652,405],{"stretchy":399},[79,16654,16655,16671],{},[76,16656,16657,16669],{},[550,16658,16659,16661],{},[84,16660,2173],{"mathvariant":86},[76,16662,16663,16665,16667],{},[84,16664,16342],{},[397,16666,817],{},[102,16668,820],{},[84,16670,359],{},[76,16672,16673,16675],{},[84,16674,2173],{"mathvariant":86},[550,16676,16677,16679],{},[84,16678,2152],{},[76,16680,16681,16683,16685],{},[84,16682,16342],{},[397,16684,817],{},[102,16686,820],{},[397,16688,990],{},[397,16690,16359],{},[397,16692,990],{},[96,16694,16695,16697],{},[84,16696,16644],{},[84,16698,16342],{},[397,16700,400],{"stretchy":399},[84,16702,2152],{},[397,16704,405],{"stretchy":399},[84,16706,359],{},[106,16708,16709],{"encoding":108},"L[x] = \\frac{\\mathrm{d}^n x}{\\mathrm{d}t^n} + a_1(t)\\frac{\\mathrm{d}^{n-1}x}{\\mathrm{d}t^{n-1}} + \\cdots + a_n(t)x",[60,16711,16713,16740,16881,17093,17112],{"className":16712,"ariaHidden":114},[113],[60,16714,16716,16719,16722,16725,16728,16731,16734,16737],{"className":16715},[118],[60,16717],{"className":16718,"style":418},[122],[60,16720,16533],{"className":16721},[127,178],[60,16723,4981],{"className":16724},[131],[60,16726,359],{"className":16727},[127,178],[60,16729,5004],{"className":16730},[267],[60,16732],{"className":16733,"style":470},[469],[60,16735,448],{"className":16736},[474],[60,16738],{"className":16739,"style":470},[469],[60,16741,16743,16746,16872,16875,16878],{"className":16742},[118],[60,16744],{"className":16745,"style":16372},[122],[60,16747,16749,16752,16869],{"className":16748},[127],[60,16750],{"className":16751},[131,132],[60,16753,16755],{"className":16754},[79],[60,16756,16758,16861],{"className":16757},[139,140],[60,16759,16761,16858],{"className":16760},[144],[60,16762,16764,16807,16815],{"className":16763,"style":1046},[148],[60,16765,16766,16769],{"style":152},[60,16767],{"className":16768,"style":157},[156],[60,16770,16772],{"className":16771},[161,162,163,164],[60,16773,16775,16778],{"className":16774},[127,164],[60,16776,2173],{"className":16777},[127,3869,164],[60,16779,16781,16784],{"className":16780},[127,164],[60,16782,2152],{"className":16783},[127,178,164],[60,16785,16787],{"className":16786},[183],[60,16788,16790],{"className":16789},[139],[60,16791,16793],{"className":16792},[144],[60,16794,16796],{"className":16795,"style":1082},[148],[60,16797,16798,16801],{"style":1085},[60,16799],{"className":16800,"style":200},[156],[60,16802,16804],{"className":16803},[161,204,205,164],[60,16805,16342],{"className":16806},[127,178,164],[60,16808,16809,16812],{"style":225},[60,16810],{"className":16811,"style":157},[156],[60,16813],{"className":16814,"style":233},[232],[60,16816,16817,16820],{"style":1105},[60,16818],{"className":16819,"style":157},[156],[60,16821,16823],{"className":16822},[161,162,163,164],[60,16824,16826,16855],{"className":16825},[127,164],[60,16827,16829,16832],{"className":16828},[127,164],[60,16830,2173],{"className":16831},[127,3869,164],[60,16833,16835],{"className":16834},[183],[60,16836,16838],{"className":16837},[139],[60,16839,16841],{"className":16840},[144],[60,16842,16844],{"className":16843,"style":1139},[148],[60,16845,16846,16849],{"style":1142},[60,16847],{"className":16848,"style":200},[156],[60,16850,16852],{"className":16851},[161,204,205,164],[60,16853,16342],{"className":16854},[127,178,164],[60,16856,359],{"className":16857},[127,178,164],[60,16859,213],{"className":16860},[212],[60,16862,16864],{"className":16863},[144],[60,16865,16867],{"className":16866,"style":3907},[148],[60,16868],{},[60,16870],{"className":16871},[267,132],[60,16873],{"className":16874,"style":924},[469],[60,16876,990],{"className":16877},[928],[60,16879],{"className":16880,"style":924},[469],[60,16882,16884,16888,16928,16931,16934,16937,17084,17087,17090],{"className":16883},[118],[60,16885],{"className":16886,"style":16887},[122],"height:1.3629em;vertical-align:-0.345em;",[60,16889,16891,16894],{"className":16890},[127],[60,16892,16644],{"className":16893},[127,178],[60,16895,16897],{"className":16896},[183],[60,16898,16900,16920],{"className":16899},[139,140],[60,16901,16903,16917],{"className":16902},[144],[60,16904,16906],{"className":16905,"style":318},[148],[60,16907,16908,16911],{"style":1940},[60,16909],{"className":16910,"style":325},[156],[60,16912,16914],{"className":16913},[161,162,163,164],[60,16915,820],{"className":16916},[127,164],[60,16918,213],{"className":16919},[212],[60,16921,16923],{"className":16922},[144],[60,16924,16926],{"className":16925,"style":341},[148],[60,16927],{},[60,16929,400],{"className":16930},[131],[60,16932,2152],{"className":16933},[127,178],[60,16935,405],{"className":16936},[267],[60,16938,16940,16943,17081],{"className":16939},[127],[60,16941],{"className":16942},[131,132],[60,16944,16946],{"className":16945},[79],[60,16947,16949,17073],{"className":16948},[139,140],[60,16950,16952,17070],{"className":16951},[144],[60,16953,16956,17009,17017],{"className":16954,"style":16955},[148],"height:1.0179em;",[60,16957,16958,16961],{"style":152},[60,16959],{"className":16960,"style":157},[156],[60,16962,16964],{"className":16963},[161,162,163,164],[60,16965,16967,16970],{"className":16966},[127,164],[60,16968,2173],{"className":16969},[127,3869,164],[60,16971,16973,16976],{"className":16972},[127,164],[60,16974,2152],{"className":16975},[127,178,164],[60,16977,16979],{"className":16978},[183],[60,16980,16982],{"className":16981},[139],[60,16983,16985],{"className":16984},[144],[60,16986,16989],{"className":16987,"style":16988},[148],"height:0.7463em;",[60,16990,16991,16994],{"style":1085},[60,16992],{"className":16993,"style":200},[156],[60,16995,16997],{"className":16996},[161,204,205,164],[60,16998,17000,17003,17006],{"className":16999},[127,164],[60,17001,16342],{"className":17002},[127,178,164],[60,17004,817],{"className":17005},[928,164],[60,17007,820],{"className":17008},[127,164],[60,17010,17011,17014],{"style":225},[60,17012],{"className":17013,"style":157},[156],[60,17015],{"className":17016,"style":233},[232],[60,17018,17019,17022],{"style":1105},[60,17020],{"className":17021,"style":157},[156],[60,17023,17025],{"className":17024},[161,162,163,164],[60,17026,17028,17067],{"className":17027},[127,164],[60,17029,17031,17034],{"className":17030},[127,164],[60,17032,2173],{"className":17033},[127,3869,164],[60,17035,17037],{"className":17036},[183],[60,17038,17040],{"className":17039},[139],[60,17041,17043],{"className":17042},[144],[60,17044,17047],{"className":17045,"style":17046},[148],"height:0.8913em;",[60,17048,17049,17052],{"style":1142},[60,17050],{"className":17051,"style":200},[156],[60,17053,17055],{"className":17054},[161,204,205,164],[60,17056,17058,17061,17064],{"className":17057},[127,164],[60,17059,16342],{"className":17060},[127,178,164],[60,17062,817],{"className":17063},[928,164],[60,17065,820],{"className":17066},[127,164],[60,17068,359],{"className":17069},[127,178,164],[60,17071,213],{"className":17072},[212],[60,17074,17076],{"className":17075},[144],[60,17077,17079],{"className":17078,"style":3907},[148],[60,17080],{},[60,17082],{"className":17083},[267,132],[60,17085],{"className":17086,"style":924},[469],[60,17088,990],{"className":17089},[928],[60,17091],{"className":17092,"style":924},[469],[60,17094,17096,17100,17103,17106,17109],{"className":17095},[118],[60,17097],{"className":17098,"style":17099},[122],"height:0.6667em;vertical-align:-0.0833em;",[60,17101,16359],{"className":17102},[2326],[60,17104],{"className":17105,"style":924},[469],[60,17107,990],{"className":17108},[928],[60,17110],{"className":17111,"style":924},[469],[60,17113,17115,17118,17159,17162,17165,17168],{"className":17114},[118],[60,17116],{"className":17117,"style":418},[122],[60,17119,17121,17124],{"className":17120},[127],[60,17122,16644],{"className":17123},[127,178],[60,17125,17127],{"className":17126},[183],[60,17128,17130,17151],{"className":17129},[139,140],[60,17131,17133,17148],{"className":17132},[144],[60,17134,17137],{"className":17135,"style":17136},[148],"height:0.1514em;",[60,17138,17139,17142],{"style":1940},[60,17140],{"className":17141,"style":325},[156],[60,17143,17145],{"className":17144},[161,162,163,164],[60,17146,16342],{"className":17147},[127,178,164],[60,17149,213],{"className":17150},[212],[60,17152,17154],{"className":17153},[144],[60,17155,17157],{"className":17156,"style":341},[148],[60,17158],{},[60,17160,400],{"className":17161},[131],[60,17163,2152],{"className":17164},[127,178],[60,17166,405],{"className":17167},[267],[60,17169,359],{"className":17170},[127,178],[23,17172,17173,17176,17177,17180,17181,17518,17519,17866,17867,17895,17896],{},[26,17174,17175],{},"第二步：利用导数的“线性”性质","\n我们要知道一个常识：",[26,17178,17179],{},"和的导数 = 导数的和","。\n即 ",[60,17182,17184,17238],{"className":17183},[63],[60,17185,17187],{"className":17186},[67],[69,17188,17189],{"xmlns":71},[73,17190,17191,17235],{},[76,17192,17193,17195,17201,17203,17209,17215,17217,17225,17227],{},[397,17194,400],{"stretchy":399},[96,17196,17197,17199],{},[84,17198,359],{},[102,17200,820],{},[397,17202,990],{},[96,17204,17205,17207],{},[84,17206,359],{},[102,17208,814],{},[550,17210,17211,17213],{},[397,17212,405],{"stretchy":399},[397,17214,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,17216,448],{},[2127,17218,17219,17221,17223],{},[84,17220,359],{},[102,17222,820],{},[397,17224,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,17226,990],{},[2127,17228,17229,17231,17233],{},[84,17230,359],{},[102,17232,814],{},[397,17234,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,17236,17237],{"encoding":108},"(x_1 + x_2)' = x_1' + x_2'",[60,17239,17241,17299,17386,17458],{"className":17240,"ariaHidden":114},[113],[60,17242,17244,17247,17250,17290,17293,17296],{"className":17243},[118],[60,17245],{"className":17246,"style":418},[122],[60,17248,400],{"className":17249},[131],[60,17251,17253,17256],{"className":17252},[127],[60,17254,359],{"className":17255},[127,178],[60,17257,17259],{"className":17258},[183],[60,17260,17262,17282],{"className":17261},[139,140],[60,17263,17265,17279],{"className":17264},[144],[60,17266,17268],{"className":17267,"style":318},[148],[60,17269,17270,17273],{"style":1940},[60,17271],{"className":17272,"style":325},[156],[60,17274,17276],{"className":17275},[161,162,163,164],[60,17277,820],{"className":17278},[127,164],[60,17280,213],{"className":17281},[212],[60,17283,17285],{"className":17284},[144],[60,17286,17288],{"className":17287,"style":341},[148],[60,17289],{},[60,17291],{"className":17292,"style":924},[469],[60,17294,990],{"className":17295},[928],[60,17297],{"className":17298,"style":924},[469],[60,17300,17302,17305,17345,17377,17380,17383],{"className":17301},[118],[60,17303],{"className":17304,"style":10437},[122],[60,17306,17308,17311],{"className":17307},[127],[60,17309,359],{"className":17310},[127,178],[60,17312,17314],{"className":17313},[183],[60,17315,17317,17337],{"className":17316},[139,140],[60,17318,17320,17334],{"className":17319},[144],[60,17321,17323],{"className":17322,"style":318},[148],[60,17324,17325,17328],{"style":1940},[60,17326],{"className":17327,"style":325},[156],[60,17329,17331],{"className":17330},[161,162,163,164],[60,17332,814],{"className":17333},[127,164],[60,17335,213],{"className":17336},[212],[60,17338,17340],{"className":17339},[144],[60,17341,17343],{"className":17342,"style":341},[148],[60,17344],{},[60,17346,17348,17351],{"className":17347},[267],[60,17349,405],{"className":17350},[267],[60,17352,17354],{"className":17353},[183],[60,17355,17357],{"className":17356},[139],[60,17358,17360],{"className":17359},[144],[60,17361,17363],{"className":17362,"style":605},[148],[60,17364,17365,17368],{"style":608},[60,17366],{"className":17367,"style":325},[156],[60,17369,17371],{"className":17370},[161,162,163,164],[60,17372,17374],{"className":17373},[127,164],[60,17375,557],{"className":17376},[127,164],[60,17378],{"className":17379,"style":470},[469],[60,17381,448],{"className":17382},[474],[60,17384],{"className":17385,"style":470},[469],[60,17387,17389,17393,17449,17452,17455],{"className":17388},[118],[60,17390],{"className":17391,"style":17392},[122],"height:1em;vertical-align:-0.2481em;",[60,17394,17396,17399],{"className":17395},[127],[60,17397,359],{"className":17398},[127,178],[60,17400,17402],{"className":17401},[183],[60,17403,17405,17440],{"className":17404},[139,140],[60,17406,17408,17437],{"className":17407},[144],[60,17409,17411,17423],{"className":17410,"style":605},[148],[60,17412,17414,17417],{"style":17413},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[60,17415],{"className":17416,"style":325},[156],[60,17418,17420],{"className":17419},[161,162,163,164],[60,17421,820],{"className":17422},[127,164],[60,17424,17425,17428],{"style":608},[60,17426],{"className":17427,"style":325},[156],[60,17429,17431],{"className":17430},[161,162,163,164],[60,17432,17434],{"className":17433},[127,164],[60,17435,557],{"className":17436},[127,164],[60,17438,213],{"className":17439},[212],[60,17441,17443],{"className":17442},[144],[60,17444,17447],{"className":17445,"style":17446},[148],"height:0.2481em;",[60,17448],{},[60,17450],{"className":17451,"style":924},[469],[60,17453,990],{"className":17454},[928],[60,17456],{"className":17457,"style":924},[469],[60,17459,17461,17464],{"className":17460},[118],[60,17462],{"className":17463,"style":17392},[122],[60,17465,17467,17470],{"className":17466},[127],[60,17468,359],{"className":17469},[127,178],[60,17471,17473],{"className":17472},[183],[60,17474,17476,17510],{"className":17475},[139,140],[60,17477,17479,17507],{"className":17478},[144],[60,17480,17482,17493],{"className":17481,"style":605},[148],[60,17483,17484,17487],{"style":17413},[60,17485],{"className":17486,"style":325},[156],[60,17488,17490],{"className":17489},[161,162,163,164],[60,17491,814],{"className":17492},[127,164],[60,17494,17495,17498],{"style":608},[60,17496],{"className":17497,"style":325},[156],[60,17499,17501],{"className":17500},[161,162,163,164],[60,17502,17504],{"className":17503},[127,164],[60,17505,557],{"className":17506},[127,164],[60,17508,213],{"className":17509},[212],[60,17511,17513],{"className":17512},[144],[60,17514,17516],{"className":17515,"style":17446},[148],[60,17517],{},"，",[60,17520,17522,17588],{"className":17521},[63],[60,17523,17525],{"className":17524},[67],[69,17526,17527],{"xmlns":71},[73,17528,17529,17585],{},[76,17530,17531,17533,17539,17541,17547,17557,17559,17571,17573],{},[397,17532,400],{"stretchy":399},[96,17534,17535,17537],{},[84,17536,359],{},[102,17538,820],{},[397,17540,990],{},[96,17542,17543,17545],{},[84,17544,359],{},[102,17546,814],{},[550,17548,17549,17551],{},[397,17550,405],{"stretchy":399},[76,17552,17553,17555],{},[397,17554,557],{"mathvariant":86},[397,17556,557],{"mathvariant":86},[397,17558,448],{},[2127,17560,17561,17563,17565],{},[84,17562,359],{},[102,17564,820],{},[76,17566,17567,17569],{},[397,17568,557],{"mathvariant":86},[397,17570,557],{"mathvariant":86},[397,17572,990],{},[2127,17574,17575,17577,17579],{},[84,17576,359],{},[102,17578,814],{},[76,17580,17581,17583],{},[397,17582,557],{"mathvariant":86},[397,17584,557],{"mathvariant":86},[106,17586,17587],{"encoding":108},"(x_1 + x_2)'' = x_1'' + x_2''",[60,17589,17591,17649,17737,17806],{"className":17590,"ariaHidden":114},[113],[60,17592,17594,17597,17600,17640,17643,17646],{"className":17593},[118],[60,17595],{"className":17596,"style":418},[122],[60,17598,400],{"className":17599},[131],[60,17601,17603,17606],{"className":17602},[127],[60,17604,359],{"className":17605},[127,178],[60,17607,17609],{"className":17608},[183],[60,17610,17612,17632],{"className":17611},[139,140],[60,17613,17615,17629],{"className":17614},[144],[60,17616,17618],{"className":17617,"style":318},[148],[60,17619,17620,17623],{"style":1940},[60,17621],{"className":17622,"style":325},[156],[60,17624,17626],{"className":17625},[161,162,163,164],[60,17627,820],{"className":17628},[127,164],[60,17630,213],{"className":17631},[212],[60,17633,17635],{"className":17634},[144],[60,17636,17638],{"className":17637,"style":341},[148],[60,17639],{},[60,17641],{"className":17642,"style":924},[469],[60,17644,990],{"className":17645},[928],[60,17647],{"className":17648,"style":924},[469],[60,17650,17652,17655,17695,17728,17731,17734],{"className":17651},[118],[60,17653],{"className":17654,"style":10437},[122],[60,17656,17658,17661],{"className":17657},[127],[60,17659,359],{"className":17660},[127,178],[60,17662,17664],{"className":17663},[183],[60,17665,17667,17687],{"className":17666},[139,140],[60,17668,17670,17684],{"className":17669},[144],[60,17671,17673],{"className":17672,"style":318},[148],[60,17674,17675,17678],{"style":1940},[60,17676],{"className":17677,"style":325},[156],[60,17679,17681],{"className":17680},[161,162,163,164],[60,17682,814],{"className":17683},[127,164],[60,17685,213],{"className":17686},[212],[60,17688,17690],{"className":17689},[144],[60,17691,17693],{"className":17692,"style":341},[148],[60,17694],{},[60,17696,17698,17701],{"className":17697},[267],[60,17699,405],{"className":17700},[267],[60,17702,17704],{"className":17703},[183],[60,17705,17707],{"className":17706},[139],[60,17708,17710],{"className":17709},[144],[60,17711,17713],{"className":17712,"style":605},[148],[60,17714,17715,17718],{"style":608},[60,17716],{"className":17717,"style":325},[156],[60,17719,17721],{"className":17720},[161,162,163,164],[60,17722,17724],{"className":17723},[127,164],[60,17725,17727],{"className":17726},[127,164],"′′",[60,17729],{"className":17730,"style":470},[469],[60,17732,448],{"className":17733},[474],[60,17735],{"className":17736,"style":470},[469],[60,17738,17740,17743,17797,17800,17803],{"className":17739},[118],[60,17741],{"className":17742,"style":17392},[122],[60,17744,17746,17749],{"className":17745},[127],[60,17747,359],{"className":17748},[127,178],[60,17750,17752],{"className":17751},[183],[60,17753,17755,17789],{"className":17754},[139,140],[60,17756,17758,17786],{"className":17757},[144],[60,17759,17761,17772],{"className":17760,"style":605},[148],[60,17762,17763,17766],{"style":17413},[60,17764],{"className":17765,"style":325},[156],[60,17767,17769],{"className":17768},[161,162,163,164],[60,17770,820],{"className":17771},[127,164],[60,17773,17774,17777],{"style":608},[60,17775],{"className":17776,"style":325},[156],[60,17778,17780],{"className":17779},[161,162,163,164],[60,17781,17783],{"className":17782},[127,164],[60,17784,17727],{"className":17785},[127,164],[60,17787,213],{"className":17788},[212],[60,17790,17792],{"className":17791},[144],[60,17793,17795],{"className":17794,"style":17446},[148],[60,17796],{},[60,17798],{"className":17799,"style":924},[469],[60,17801,990],{"className":17802},[928],[60,17804],{"className":17805,"style":924},[469],[60,17807,17809,17812],{"className":17808},[118],[60,17810],{"className":17811,"style":17392},[122],[60,17813,17815,17818],{"className":17814},[127],[60,17816,359],{"className":17817},[127,178],[60,17819,17821],{"className":17820},[183],[60,17822,17824,17858],{"className":17823},[139,140],[60,17825,17827,17855],{"className":17826},[144],[60,17828,17830,17841],{"className":17829,"style":605},[148],[60,17831,17832,17835],{"style":17413},[60,17833],{"className":17834,"style":325},[156],[60,17836,17838],{"className":17837},[161,162,163,164],[60,17839,814],{"className":17840},[127,164],[60,17842,17843,17846],{"style":608},[60,17844],{"className":17845,"style":325},[156],[60,17847,17849],{"className":17848},[161,162,163,164],[60,17850,17852],{"className":17851},[127,164],[60,17853,17727],{"className":17854},[127,164],[60,17856,213],{"className":17857},[212],[60,17859,17861],{"className":17860},[144],[60,17862,17864],{"className":17863,"style":17446},[148],[60,17865],{},"，以此类推。\n这意味着运算 ",[60,17868,17870,17883],{"className":17869},[63],[60,17871,17873],{"className":17872},[67],[69,17874,17875],{"xmlns":71},[73,17876,17877,17881],{},[76,17878,17879],{},[84,17880,16533],{},[106,17882,16533],{"encoding":108},[60,17884,17886],{"className":17885,"ariaHidden":114},[113],[60,17887,17889,17892],{"className":17888},[118],[60,17890],{"className":17891,"style":532},[122],[60,17893,16533],{"className":17894},[127,178]," 也是线性的：\n",[60,17897,17899,17959],{"className":17898},[63],[60,17900,17902],{"className":17901},[67],[69,17903,17904],{"xmlns":71},[73,17905,17906,17956],{},[76,17907,17908,17910,17912,17918,17920,17926,17928,17930,17932,17934,17940,17942,17944,17946,17948,17954],{},[84,17909,16533],{},[397,17911,4981],{"stretchy":399},[96,17913,17914,17916],{},[84,17915,359],{},[102,17917,820],{},[397,17919,990],{},[96,17921,17922,17924],{},[84,17923,359],{},[102,17925,814],{},[397,17927,5004],{"stretchy":399},[397,17929,448],{},[84,17931,16533],{},[397,17933,4981],{"stretchy":399},[96,17935,17936,17938],{},[84,17937,359],{},[102,17939,820],{},[397,17941,5004],{"stretchy":399},[397,17943,990],{},[84,17945,16533],{},[397,17947,4981],{"stretchy":399},[96,17949,17950,17952],{},[84,17951,359],{},[102,17953,814],{},[397,17955,5004],{"stretchy":399},[106,17957,17958],{"encoding":108},"L[x_1 + x_2] = L[x_1] + L[x_2]",[60,17960,17962,18023,18081,18145],{"className":17961,"ariaHidden":114},[113],[60,17963,17965,17968,17971,17974,18014,18017,18020],{"className":17964},[118],[60,17966],{"className":17967,"style":418},[122],[60,17969,16533],{"className":17970},[127,178],[60,17972,4981],{"className":17973},[131],[60,17975,17977,17980],{"className":17976},[127],[60,17978,359],{"className":17979},[127,178],[60,17981,17983],{"className":17982},[183],[60,17984,17986,18006],{"className":17985},[139,140],[60,17987,17989,18003],{"className":17988},[144],[60,17990,17992],{"className":17991,"style":318},[148],[60,17993,17994,17997],{"style":1940},[60,17995],{"className":17996,"style":325},[156],[60,17998,18000],{"className":17999},[161,162,163,164],[60,18001,820],{"className":18002},[127,164],[60,18004,213],{"className":18005},[212],[60,18007,18009],{"className":18008},[144],[60,18010,18012],{"className":18011,"style":341},[148],[60,18013],{},[60,18015],{"className":18016,"style":924},[469],[60,18018,990],{"className":18019},[928],[60,18021],{"className":18022,"style":924},[469],[60,18024,18026,18029,18069,18072,18075,18078],{"className":18025},[118],[60,18027],{"className":18028,"style":418},[122],[60,18030,18032,18035],{"className":18031},[127],[60,18033,359],{"className":18034},[127,178],[60,18036,18038],{"className":18037},[183],[60,18039,18041,18061],{"className":18040},[139,140],[60,18042,18044,18058],{"className":18043},[144],[60,18045,18047],{"className":18046,"style":318},[148],[60,18048,18049,18052],{"style":1940},[60,18050],{"className":18051,"style":325},[156],[60,18053,18055],{"className":18054},[161,162,163,164],[60,18056,814],{"className":18057},[127,164],[60,18059,213],{"className":18060},[212],[60,18062,18064],{"className":18063},[144],[60,18065,18067],{"className":18066,"style":341},[148],[60,18068],{},[60,18070,5004],{"className":18071},[267],[60,18073],{"className":18074,"style":470},[469],[60,18076,448],{"className":18077},[474],[60,18079],{"className":18080,"style":470},[469],[60,18082,18084,18087,18090,18093,18133,18136,18139,18142],{"className":18083},[118],[60,18085],{"className":18086,"style":418},[122],[60,18088,16533],{"className":18089},[127,178],[60,18091,4981],{"className":18092},[131],[60,18094,18096,18099],{"className":18095},[127],[60,18097,359],{"className":18098},[127,178],[60,18100,18102],{"className":18101},[183],[60,18103,18105,18125],{"className":18104},[139,140],[60,18106,18108,18122],{"className":18107},[144],[60,18109,18111],{"className":18110,"style":318},[148],[60,18112,18113,18116],{"style":1940},[60,18114],{"className":18115,"style":325},[156],[60,18117,18119],{"className":18118},[161,162,163,164],[60,18120,820],{"className":18121},[127,164],[60,18123,213],{"className":18124},[212],[60,18126,18128],{"className":18127},[144],[60,18129,18131],{"className":18130,"style":341},[148],[60,18132],{},[60,18134,5004],{"className":18135},[267],[60,18137],{"className":18138,"style":924},[469],[60,18140,990],{"className":18141},[928],[60,18143],{"className":18144,"style":924},[469],[60,18146,18148,18151,18154,18157,18197],{"className":18147},[118],[60,18149],{"className":18150,"style":418},[122],[60,18152,16533],{"className":18153},[127,178],[60,18155,4981],{"className":18156},[131],[60,18158,18160,18163],{"className":18159},[127],[60,18161,359],{"className":18162},[127,178],[60,18164,18166],{"className":18165},[183],[60,18167,18169,18189],{"className":18168},[139,140],[60,18170,18172,18186],{"className":18171},[144],[60,18173,18175],{"className":18174,"style":318},[148],[60,18176,18177,18180],{"style":1940},[60,18178],{"className":18179,"style":325},[156],[60,18181,18183],{"className":18182},[161,162,163,164],[60,18184,814],{"className":18185},[127,164],[60,18187,213],{"className":18188},[212],[60,18190,18192],{"className":18191},[144],[60,18193,18195],{"className":18194,"style":341},[148],[60,18196],{},[60,18198,5004],{"className":18199},[267],[23,18201,18202,18205],{},[26,18203,18204],{},"第三步：代入题目条件","\n题目告诉我们：",[30,18207,18208,18470],{},[33,18209,18210,18279,18280],{},[60,18211,18213,18230],{"className":18212},[63],[60,18214,18216],{"className":18215},[67],[69,18217,18218],{"xmlns":71},[73,18219,18220,18228],{},[76,18221,18222],{},[96,18223,18224,18226],{},[84,18225,359],{},[102,18227,820],{},[106,18229,15777],{"encoding":108},[60,18231,18233],{"className":18232,"ariaHidden":114},[113],[60,18234,18236,18239],{"className":18235},[118],[60,18237],{"className":18238,"style":2734},[122],[60,18240,18242,18245],{"className":18241},[127],[60,18243,359],{"className":18244},[127,178],[60,18246,18248],{"className":18247},[183],[60,18249,18251,18271],{"className":18250},[139,140],[60,18252,18254,18268],{"className":18253},[144],[60,18255,18257],{"className":18256,"style":318},[148],[60,18258,18259,18262],{"style":1940},[60,18260],{"className":18261,"style":325},[156],[60,18263,18265],{"className":18264},[161,162,163,164],[60,18266,820],{"className":18267},[127,164],[60,18269,213],{"className":18270},[212],[60,18272,18274],{"className":18273},[144],[60,18275,18277],{"className":18276,"style":341},[148],[60,18278],{}," 是第一个方程的解 ",[60,18281,18283,18329],{"className":18282},[63],[60,18284,18286],{"className":18285},[67],[69,18287,18288],{"xmlns":71},[73,18289,18290,18326],{},[76,18291,18292,18295,18298,18300,18302,18304,18310,18312,18314,18320,18322,18324],{},[13095,18293,18294],{},"  ",[397,18296,18297],{},"⟹",[13095,18299,18294],{},[84,18301,16533],{},[397,18303,4981],{"stretchy":399},[96,18305,18306,18308],{},[84,18307,359],{},[102,18309,820],{},[397,18311,5004],{"stretchy":399},[397,18313,448],{},[96,18315,18316,18318],{},[84,18317,562],{},[102,18319,820],{},[397,18321,400],{"stretchy":399},[84,18323,2152],{},[397,18325,405],{"stretchy":399},[106,18327,18328],{"encoding":108},"\\implies L[x_1] = f_1(t)",[60,18330,18332,18351,18415],{"className":18331,"ariaHidden":114},[113],[60,18333,18335,18339,18342,18345,18348],{"className":18334},[118],[60,18336],{"className":18337,"style":18338},[122],"height:0.549em;vertical-align:-0.024em;",[60,18340],{"className":18341,"style":470},[469],[60,18343,18297],{"className":18344},[474],[60,18346],{"className":18347,"style":470},[469],[60,18349],{"className":18350,"style":470},[469],[60,18352,18354,18357,18360,18363,18403,18406,18409,18412],{"className":18353},[118],[60,18355],{"className":18356,"style":418},[122],[60,18358,16533],{"className":18359},[127,178],[60,18361,4981],{"className":18362},[131],[60,18364,18366,18369],{"className":18365},[127],[60,18367,359],{"className":18368},[127,178],[60,18370,18372],{"className":18371},[183],[60,18373,18375,18395],{"className":18374},[139,140],[60,18376,18378,18392],{"className":18377},[144],[60,18379,18381],{"className":18380,"style":318},[148],[60,18382,18383,18386],{"style":1940},[60,18384],{"className":18385,"style":325},[156],[60,18387,18389],{"className":18388},[161,162,163,164],[60,18390,820],{"className":18391},[127,164],[60,18393,213],{"className":18394},[212],[60,18396,18398],{"className":18397},[144],[60,18399,18401],{"className":18400,"style":341},[148],[60,18402],{},[60,18404,5004],{"className":18405},[267],[60,18407],{"className":18408,"style":470},[469],[60,18410,448],{"className":18411},[474],[60,18413],{"className":18414,"style":470},[469],[60,18416,18418,18421,18461,18464,18467],{"className":18417},[118],[60,18419],{"className":18420,"style":418},[122],[60,18422,18424,18427],{"className":18423},[127],[60,18425,562],{"className":18426,"style":639},[127,178],[60,18428,18430],{"className":18429},[183],[60,18431,18433,18453],{"className":18432},[139,140],[60,18434,18436,18450],{"className":18435},[144],[60,18437,18439],{"className":18438,"style":318},[148],[60,18440,18441,18444],{"style":15878},[60,18442],{"className":18443,"style":325},[156],[60,18445,18447],{"className":18446},[161,162,163,164],[60,18448,820],{"className":18449},[127,164],[60,18451,213],{"className":18452},[212],[60,18454,18456],{"className":18455},[144],[60,18457,18459],{"className":18458,"style":341},[148],[60,18460],{},[60,18462,400],{"className":18463},[131],[60,18465,2152],{"className":18466},[127,178],[60,18468,405],{"className":18469},[267],[33,18471,18472,18541,18542],{},[60,18473,18475,18492],{"className":18474},[63],[60,18476,18478],{"className":18477},[67],[69,18479,18480],{"xmlns":71},[73,18481,18482,18490],{},[76,18483,18484],{},[96,18485,18486,18488],{},[84,18487,359],{},[102,18489,814],{},[106,18491,15920],{"encoding":108},[60,18493,18495],{"className":18494,"ariaHidden":114},[113],[60,18496,18498,18501],{"className":18497},[118],[60,18499],{"className":18500,"style":2734},[122],[60,18502,18504,18507],{"className":18503},[127],[60,18505,359],{"className":18506},[127,178],[60,18508,18510],{"className":18509},[183],[60,18511,18513,18533],{"className":18512},[139,140],[60,18514,18516,18530],{"className":18515},[144],[60,18517,18519],{"className":18518,"style":318},[148],[60,18520,18521,18524],{"style":1940},[60,18522],{"className":18523,"style":325},[156],[60,18525,18527],{"className":18526},[161,162,163,164],[60,18528,814],{"className":18529},[127,164],[60,18531,213],{"className":18532},[212],[60,18534,18536],{"className":18535},[144],[60,18537,18539],{"className":18538,"style":341},[148],[60,18540],{}," 是第二个方程的解 ",[60,18543,18545,18589],{"className":18544},[63],[60,18546,18548],{"className":18547},[67],[69,18549,18550],{"xmlns":71},[73,18551,18552,18586],{},[76,18553,18554,18556,18558,18560,18562,18564,18570,18572,18574,18580,18582,18584],{},[13095,18555,18294],{},[397,18557,18297],{},[13095,18559,18294],{},[84,18561,16533],{},[397,18563,4981],{"stretchy":399},[96,18565,18566,18568],{},[84,18567,359],{},[102,18569,814],{},[397,18571,5004],{"stretchy":399},[397,18573,448],{},[96,18575,18576,18578],{},[84,18577,562],{},[102,18579,814],{},[397,18581,400],{"stretchy":399},[84,18583,2152],{},[397,18585,405],{"stretchy":399},[106,18587,18588],{"encoding":108},"\\implies L[x_2] = f_2(t)",[60,18590,18592,18610,18674],{"className":18591,"ariaHidden":114},[113],[60,18593,18595,18598,18601,18604,18607],{"className":18594},[118],[60,18596],{"className":18597,"style":18338},[122],[60,18599],{"className":18600,"style":470},[469],[60,18602,18297],{"className":18603},[474],[60,18605],{"className":18606,"style":470},[469],[60,18608],{"className":18609,"style":470},[469],[60,18611,18613,18616,18619,18622,18662,18665,18668,18671],{"className":18612},[118],[60,18614],{"className":18615,"style":418},[122],[60,18617,16533],{"className":18618},[127,178],[60,18620,4981],{"className":18621},[131],[60,18623,18625,18628],{"className":18624},[127],[60,18626,359],{"className":18627},[127,178],[60,18629,18631],{"className":18630},[183],[60,18632,18634,18654],{"className":18633},[139,140],[60,18635,18637,18651],{"className":18636},[144],[60,18638,18640],{"className":18639,"style":318},[148],[60,18641,18642,18645],{"style":1940},[60,18643],{"className":18644,"style":325},[156],[60,18646,18648],{"className":18647},[161,162,163,164],[60,18649,814],{"className":18650},[127,164],[60,18652,213],{"className":18653},[212],[60,18655,18657],{"className":18656},[144],[60,18658,18660],{"className":18659,"style":341},[148],[60,18661],{},[60,18663,5004],{"className":18664},[267],[60,18666],{"className":18667,"style":470},[469],[60,18669,448],{"className":18670},[474],[60,18672],{"className":18673,"style":470},[469],[60,18675,18677,18680,18720,18723,18726],{"className":18676},[118],[60,18678],{"className":18679,"style":418},[122],[60,18681,18683,18686],{"className":18682},[127],[60,18684,562],{"className":18685,"style":639},[127,178],[60,18687,18689],{"className":18688},[183],[60,18690,18692,18712],{"className":18691},[139,140],[60,18693,18695,18709],{"className":18694},[144],[60,18696,18698],{"className":18697,"style":318},[148],[60,18699,18700,18703],{"style":15878},[60,18701],{"className":18702,"style":325},[156],[60,18704,18706],{"className":18705},[161,162,163,164],[60,18707,814],{"className":18708},[127,164],[60,18710,213],{"className":18711},[212],[60,18713,18715],{"className":18714},[144],[60,18716,18718],{"className":18717,"style":341},[148],[60,18719],{},[60,18721,400],{"className":18722},[131],[60,18724,2152],{"className":18725},[127,178],[60,18727,405],{"className":18728},[267],[23,18730,18731,18734,18735,18868,18869,19001,19002,19030,19031,19859],{},[26,18732,18733],{},"第四步：得出结论","\n我们要验证 ",[60,18736,18738,18764],{"className":18737},[63],[60,18739,18741],{"className":18740},[67],[69,18742,18743],{"xmlns":71},[73,18744,18745,18761],{},[76,18746,18747,18753,18755],{},[96,18748,18749,18751],{},[84,18750,359],{},[102,18752,820],{},[397,18754,990],{},[96,18756,18757,18759],{},[84,18758,359],{},[102,18760,814],{},[106,18762,18763],{"encoding":108},"x_1 + x_2",[60,18765,18767,18822],{"className":18766,"ariaHidden":114},[113],[60,18768,18770,18773,18813,18816,18819],{"className":18769},[118],[60,18771],{"className":18772,"style":16079},[122],[60,18774,18776,18779],{"className":18775},[127],[60,18777,359],{"className":18778},[127,178],[60,18780,18782],{"className":18781},[183],[60,18783,18785,18805],{"className":18784},[139,140],[60,18786,18788,18802],{"className":18787},[144],[60,18789,18791],{"className":18790,"style":318},[148],[60,18792,18793,18796],{"style":1940},[60,18794],{"className":18795,"style":325},[156],[60,18797,18799],{"className":18798},[161,162,163,164],[60,18800,820],{"className":18801},[127,164],[60,18803,213],{"className":18804},[212],[60,18806,18808],{"className":18807},[144],[60,18809,18811],{"className":18810,"style":341},[148],[60,18812],{},[60,18814],{"className":18815,"style":924},[469],[60,18817,990],{"className":18818},[928],[60,18820],{"className":18821,"style":924},[469],[60,18823,18825,18828],{"className":18824},[118],[60,18826],{"className":18827,"style":2734},[122],[60,18829,18831,18834],{"className":18830},[127],[60,18832,359],{"className":18833},[127,178],[60,18835,18837],{"className":18836},[183],[60,18838,18840,18860],{"className":18839},[139,140],[60,18841,18843,18857],{"className":18842},[144],[60,18844,18846],{"className":18845,"style":318},[148],[60,18847,18848,18851],{"style":1940},[60,18849],{"className":18850,"style":325},[156],[60,18852,18854],{"className":18853},[161,162,163,164],[60,18855,814],{"className":18856},[127,164],[60,18858,213],{"className":18859},[212],[60,18861,18863],{"className":18862},[144],[60,18864,18866],{"className":18865,"style":341},[148],[60,18867],{}," 是不是第三个方程的解，就是把 ",[60,18870,18872,18897],{"className":18871},[63],[60,18873,18875],{"className":18874},[67],[69,18876,18877],{"xmlns":71},[73,18878,18879,18895],{},[76,18880,18881,18887,18889],{},[96,18882,18883,18885],{},[84,18884,359],{},[102,18886,820],{},[397,18888,990],{},[96,18890,18891,18893],{},[84,18892,359],{},[102,18894,814],{},[106,18896,16069],{"encoding":108},[60,18898,18900,18955],{"className":18899,"ariaHidden":114},[113],[60,18901,18903,18906,18946,18949,18952],{"className":18902},[118],[60,18904],{"className":18905,"style":16079},[122],[60,18907,18909,18912],{"className":18908},[127],[60,18910,359],{"className":18911},[127,178],[60,18913,18915],{"className":18914},[183],[60,18916,18918,18938],{"className":18917},[139,140],[60,18919,18921,18935],{"className":18920},[144],[60,18922,18924],{"className":18923,"style":318},[148],[60,18925,18926,18929],{"style":1940},[60,18927],{"className":18928,"style":325},[156],[60,18930,18932],{"className":18931},[161,162,163,164],[60,18933,820],{"className":18934},[127,164],[60,18936,213],{"className":18937},[212],[60,18939,18941],{"className":18940},[144],[60,18942,18944],{"className":18943,"style":341},[148],[60,18945],{},[60,18947],{"className":18948,"style":924},[469],[60,18950,990],{"className":18951},[928],[60,18953],{"className":18954,"style":924},[469],[60,18956,18958,18961],{"className":18957},[118],[60,18959],{"className":18960,"style":2734},[122],[60,18962,18964,18967],{"className":18963},[127],[60,18965,359],{"className":18966},[127,178],[60,18968,18970],{"className":18969},[183],[60,18971,18973,18993],{"className":18972},[139,140],[60,18974,18976,18990],{"className":18975},[144],[60,18977,18979],{"className":18978,"style":318},[148],[60,18980,18981,18984],{"style":1940},[60,18982],{"className":18983,"style":325},[156],[60,18985,18987],{"className":18986},[161,162,163,164],[60,18988,814],{"className":18989},[127,164],[60,18991,213],{"className":18992},[212],[60,18994,18996],{"className":18995},[144],[60,18997,18999],{"className":18998,"style":341},[148],[60,19000],{}," 塞进 ",[60,19003,19005,19018],{"className":19004},[63],[60,19006,19008],{"className":19007},[67],[69,19009,19010],{"xmlns":71},[73,19011,19012,19016],{},[76,19013,19014],{},[84,19015,16533],{},[106,19017,16533],{"encoding":108},[60,19019,19021],{"className":19020,"ariaHidden":114},[113],[60,19022,19024,19027],{"className":19023},[118],[60,19025],{"className":19026,"style":532},[122],[60,19028,16533],{"className":19029},[127,178]," 里看看：\n",[60,19032,19034,19168],{"className":19033},[63],[60,19035,19037],{"className":19036},[67],[69,19038,19039],{"xmlns":71},[73,19040,19041,19165],{},[76,19042,19043,19045,19047,19053,19055,19061,19063,19065,19101,19103,19137,19139,19145,19147,19149,19151,19153,19159,19161,19163],{},[84,19044,16533],{},[397,19046,4981],{"stretchy":399},[96,19048,19049,19051],{},[84,19050,359],{},[102,19052,820],{},[397,19054,990],{},[96,19056,19057,19059],{},[84,19058,359],{},[102,19060,814],{},[397,19062,5004],{"stretchy":399},[397,19064,448],{},[19066,19067,19068,19087],"munder",{},[19066,19069,19070,19084],{},[76,19071,19072,19074,19076,19082],{},[84,19073,16533],{},[397,19075,4981],{"stretchy":399},[96,19077,19078,19080],{},[84,19079,359],{},[102,19081,820],{},[397,19083,5004],{"stretchy":399},[397,19085,19086],{"stretchy":114},"⏟",[76,19088,19089,19095,19097,19099],{},[96,19090,19091,19093],{},[84,19092,562],{},[102,19094,820],{},[397,19096,400],{"stretchy":399},[84,19098,2152],{},[397,19100,405],{"stretchy":399},[397,19102,990],{},[19066,19104,19105,19123],{},[19066,19106,19107,19121],{},[76,19108,19109,19111,19113,19119],{},[84,19110,16533],{},[397,19112,4981],{"stretchy":399},[96,19114,19115,19117],{},[84,19116,359],{},[102,19118,814],{},[397,19120,5004],{"stretchy":399},[397,19122,19086],{"stretchy":114},[76,19124,19125,19131,19133,19135],{},[96,19126,19127,19129],{},[84,19128,562],{},[102,19130,814],{},[397,19132,400],{"stretchy":399},[84,19134,2152],{},[397,19136,405],{"stretchy":399},[397,19138,448],{},[96,19140,19141,19143],{},[84,19142,562],{},[102,19144,820],{},[397,19146,400],{"stretchy":399},[84,19148,2152],{},[397,19150,405],{"stretchy":399},[397,19152,990],{},[96,19154,19155,19157],{},[84,19156,562],{},[102,19158,814],{},[397,19160,400],{"stretchy":399},[84,19162,2152],{},[397,19164,405],{"stretchy":399},[106,19166,19167],{"encoding":108},"L[x_1 + x_2] = \\underbrace{L[x_1]}_{f_1(t)} + \\underbrace{L[x_2]}_{f_2(t)} = f_1(t) + f_2(t)",[60,19169,19171,19232,19290,19527,19740,19804],{"className":19170,"ariaHidden":114},[113],[60,19172,19174,19177,19180,19183,19223,19226,19229],{"className":19173},[118],[60,19175],{"className":19176,"style":418},[122],[60,19178,16533],{"className":19179},[127,178],[60,19181,4981],{"className":19182},[131],[60,19184,19186,19189],{"className":19185},[127],[60,19187,359],{"className":19188},[127,178],[60,19190,19192],{"className":19191},[183],[60,19193,19195,19215],{"className":19194},[139,140],[60,19196,19198,19212],{"className":19197},[144],[60,19199,19201],{"className":19200,"style":318},[148],[60,19202,19203,19206],{"style":1940},[60,19204],{"className":19205,"style":325},[156],[60,19207,19209],{"className":19208},[161,162,163,164],[60,19210,820],{"className":19211},[127,164],[60,19213,213],{"className":19214},[212],[60,19216,19218],{"className":19217},[144],[60,19219,19221],{"className":19220,"style":341},[148],[60,19222],{},[60,19224],{"className":19225,"style":924},[469],[60,19227,990],{"className":19228},[928],[60,19230],{"className":19231,"style":924},[469],[60,19233,19235,19238,19278,19281,19284,19287],{"className":19234},[118],[60,19236],{"className":19237,"style":418},[122],[60,19239,19241,19244],{"className":19240},[127],[60,19242,359],{"className":19243},[127,178],[60,19245,19247],{"className":19246},[183],[60,19248,19250,19270],{"className":19249},[139,140],[60,19251,19253,19267],{"className":19252},[144],[60,19254,19256],{"className":19255,"style":318},[148],[60,19257,19258,19261],{"style":1940},[60,19259],{"className":19260,"style":325},[156],[60,19262,19264],{"className":19263},[161,162,163,164],[60,19265,814],{"className":19266},[127,164],[60,19268,213],{"className":19269},[212],[60,19271,19273],{"className":19272},[144],[60,19274,19276],{"className":19275,"style":341},[148],[60,19277],{},[60,19279,5004],{"className":19280},[267],[60,19282],{"className":19283,"style":470},[469],[60,19285,448],{"className":19286},[474],[60,19288],{"className":19289,"style":470},[469],[60,19291,19293,19297,19518,19521,19524],{"className":19292},[118],[60,19294],{"className":19295,"style":19296},[122],"height:2.548em;vertical-align:-1.798em;",[60,19298,19300],{"className":19299},[2326,19066],[60,19301,19303,19509],{"className":19302},[139,140],[60,19304,19306,19506],{"className":19305},[144],[60,19307,19310,19372],{"className":19308,"style":19309},[148],"height:0.75em;",[60,19311,19313,19316],{"style":19312},"top:-1.377em;",[60,19314],{"className":19315,"style":157},[156],[60,19317,19319],{"className":19318},[161,162,163,164],[60,19320,19322,19363,19366,19369],{"className":19321},[127,164],[60,19323,19325,19328],{"className":19324},[127,164],[60,19326,562],{"className":19327,"style":639},[127,178,164],[60,19329,19331],{"className":19330},[183],[60,19332,19334,19355],{"className":19333},[139,140],[60,19335,19337,19352],{"className":19336},[144],[60,19338,19340],{"className":19339,"style":193},[148],[60,19341,19343,19346],{"style":19342},"top:-2.357em;margin-left:-0.1076em;margin-right:0.0714em;",[60,19344],{"className":19345,"style":200},[156],[60,19347,19349],{"className":19348},[161,204,205,164],[60,19350,820],{"className":19351},[127,164],[60,19353,213],{"className":19354},[212],[60,19356,19358],{"className":19357},[144],[60,19359,19361],{"className":19360,"style":220},[148],[60,19362],{},[60,19364,400],{"className":19365},[131,164],[60,19367,2152],{"className":19368},[127,178,164],[60,19370,405],{"className":19371},[267,164],[60,19373,19375,19378],{"style":19374},"top:-3em;",[60,19376],{"className":19377,"style":157},[156],[60,19379,19381],{"className":19380},[2326,19066],[60,19382,19384,19497],{"className":19383},[139,140],[60,19385,19387,19494],{"className":19386},[144],[60,19388,19390,19437],{"className":19389,"style":19309},[148],[60,19391,19395,19398],{"className":19392,"style":19394},[19393],"svg-align","top:-2.102em;",[60,19396],{"className":19397,"style":157},[156],[60,19399,19403,19417,19427],{"className":19400,"style":19402},[19401],"katex-stretchy","height:0.548em;min-width:1.6em;",[60,19404,19408],{"className":19405,"style":19407},[19406],"brace-left","height:0.548em;",[11945,19409,19414],{"xmlns":11947,"width":19410,"height":19411,"viewBox":19412,"preserveAspectRatio":19413},"400em","0.548em","0 0 400000 548","xMinYMin slice",[11952,19415],{"d":19416},"M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z",[60,19418,19421],{"className":19419,"style":19407},[19420],"brace-center",[11945,19422,19424],{"xmlns":11947,"width":19410,"height":19411,"viewBox":19412,"preserveAspectRatio":19423},"xMidYMin slice",[11952,19425],{"d":19426},"M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z",[60,19428,19431],{"className":19429,"style":19407},[19430],"brace-right",[11945,19432,19434],{"xmlns":11947,"width":19410,"height":19411,"viewBox":19412,"preserveAspectRatio":19433},"xMaxYMin slice",[11952,19435],{"d":19436},"M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z",[60,19438,19439,19442],{"style":19374},[60,19440],{"className":19441,"style":157},[156],[60,19443,19445,19448,19451,19491],{"className":19444},[127],[60,19446,16533],{"className":19447},[127,178],[60,19449,4981],{"className":19450},[131],[60,19452,19454,19457],{"className":19453},[127],[60,19455,359],{"className":19456},[127,178],[60,19458,19460],{"className":19459},[183],[60,19461,19463,19483],{"className":19462},[139,140],[60,19464,19466,19480],{"className":19465},[144],[60,19467,19469],{"className":19468,"style":318},[148],[60,19470,19471,19474],{"style":1940},[60,19472],{"className":19473,"style":325},[156],[60,19475,19477],{"className":19476},[161,162,163,164],[60,19478,820],{"className":19479},[127,164],[60,19481,213],{"className":19482},[212],[60,19484,19486],{"className":19485},[144],[60,19487,19489],{"className":19488,"style":341},[148],[60,19490],{},[60,19492,5004],{"className":19493},[267],[60,19495,213],{"className":19496},[212],[60,19498,19500],{"className":19499},[144],[60,19501,19504],{"className":19502,"style":19503},[148],"height:0.898em;",[60,19505],{},[60,19507,213],{"className":19508},[212],[60,19510,19512],{"className":19511},[144],[60,19513,19516],{"className":19514,"style":19515},[148],"height:1.798em;",[60,19517],{},[60,19519],{"className":19520,"style":924},[469],[60,19522,990],{"className":19523},[928],[60,19525],{"className":19526,"style":924},[469],[60,19528,19530,19533,19731,19734,19737],{"className":19529},[118],[60,19531],{"className":19532,"style":19296},[122],[60,19534,19536],{"className":19535},[2326,19066],[60,19537,19539,19723],{"className":19538},[139,140],[60,19540,19542,19720],{"className":19541},[144],[60,19543,19545,19605],{"className":19544,"style":19309},[148],[60,19546,19547,19550],{"style":19312},[60,19548],{"className":19549,"style":157},[156],[60,19551,19553],{"className":19552},[161,162,163,164],[60,19554,19556,19596,19599,19602],{"className":19555},[127,164],[60,19557,19559,19562],{"className":19558},[127,164],[60,19560,562],{"className":19561,"style":639},[127,178,164],[60,19563,19565],{"className":19564},[183],[60,19566,19568,19588],{"className":19567},[139,140],[60,19569,19571,19585],{"className":19570},[144],[60,19572,19574],{"className":19573,"style":193},[148],[60,19575,19576,19579],{"style":19342},[60,19577],{"className":19578,"style":200},[156],[60,19580,19582],{"className":19581},[161,204,205,164],[60,19583,814],{"className":19584},[127,164],[60,19586,213],{"className":19587},[212],[60,19589,19591],{"className":19590},[144],[60,19592,19594],{"className":19593,"style":220},[148],[60,19595],{},[60,19597,400],{"className":19598},[131,164],[60,19600,2152],{"className":19601},[127,178,164],[60,19603,405],{"className":19604},[267,164],[60,19606,19607,19610],{"style":19374},[60,19608],{"className":19609,"style":157},[156],[60,19611,19613],{"className":19612},[2326,19066],[60,19614,19616,19712],{"className":19615},[139,140],[60,19617,19619,19709],{"className":19618},[144],[60,19620,19622,19652],{"className":19621,"style":19309},[148],[60,19623,19625,19628],{"className":19624,"style":19394},[19393],[60,19626],{"className":19627,"style":157},[156],[60,19629,19631,19638,19645],{"className":19630,"style":19402},[19401],[60,19632,19634],{"className":19633,"style":19407},[19406],[11945,19635,19636],{"xmlns":11947,"width":19410,"height":19411,"viewBox":19412,"preserveAspectRatio":19413},[11952,19637],{"d":19416},[60,19639,19641],{"className":19640,"style":19407},[19420],[11945,19642,19643],{"xmlns":11947,"width":19410,"height":19411,"viewBox":19412,"preserveAspectRatio":19423},[11952,19644],{"d":19426},[60,19646,19648],{"className":19647,"style":19407},[19430],[11945,19649,19650],{"xmlns":11947,"width":19410,"height":19411,"viewBox":19412,"preserveAspectRatio":19433},[11952,19651],{"d":19436},[60,19653,19654,19657],{"style":19374},[60,19655],{"className":19656,"style":157},[156],[60,19658,19660,19663,19666,19706],{"className":19659},[127],[60,19661,16533],{"className":19662},[127,178],[60,19664,4981],{"className":19665},[131],[60,19667,19669,19672],{"className":19668},[127],[60,19670,359],{"className":19671},[127,178],[60,19673,19675],{"className":19674},[183],[60,19676,19678,19698],{"className":19677},[139,140],[60,19679,19681,19695],{"className":19680},[144],[60,19682,19684],{"className":19683,"style":318},[148],[60,19685,19686,19689],{"style":1940},[60,19687],{"className":19688,"style":325},[156],[60,19690,19692],{"className":19691},[161,162,163,164],[60,19693,814],{"className":19694},[127,164],[60,19696,213],{"className":19697},[212],[60,19699,19701],{"className":19700},[144],[60,19702,19704],{"className":19703,"style":341},[148],[60,19705],{},[60,19707,5004],{"className":19708},[267],[60,19710,213],{"className":19711},[212],[60,19713,19715],{"className":19714},[144],[60,19716,19718],{"className":19717,"style":19503},[148],[60,19719],{},[60,19721,213],{"className":19722},[212],[60,19724,19726],{"className":19725},[144],[60,19727,19729],{"className":19728,"style":19515},[148],[60,19730],{},[60,19732],{"className":19733,"style":470},[469],[60,19735,448],{"className":19736},[474],[60,19738],{"className":19739,"style":470},[469],[60,19741,19743,19746,19786,19789,19792,19795,19798,19801],{"className":19742},[118],[60,19744],{"className":19745,"style":418},[122],[60,19747,19749,19752],{"className":19748},[127],[60,19750,562],{"className":19751,"style":639},[127,178],[60,19753,19755],{"className":19754},[183],[60,19756,19758,19778],{"className":19757},[139,140],[60,19759,19761,19775],{"className":19760},[144],[60,19762,19764],{"className":19763,"style":318},[148],[60,19765,19766,19769],{"style":15878},[60,19767],{"className":19768,"style":325},[156],[60,19770,19772],{"className":19771},[161,162,163,164],[60,19773,820],{"className":19774},[127,164],[60,19776,213],{"className":19777},[212],[60,19779,19781],{"className":19780},[144],[60,19782,19784],{"className":19783,"style":341},[148],[60,19785],{},[60,19787,400],{"className":19788},[131],[60,19790,2152],{"className":19791},[127,178],[60,19793,405],{"className":19794},[267],[60,19796],{"className":19797,"style":924},[469],[60,19799,990],{"className":19800},[928],[60,19802],{"className":19803,"style":924},[469],[60,19805,19807,19810,19850,19853,19856],{"className":19806},[118],[60,19808],{"className":19809,"style":418},[122],[60,19811,19813,19816],{"className":19812},[127],[60,19814,562],{"className":19815,"style":639},[127,178],[60,19817,19819],{"className":19818},[183],[60,19820,19822,19842],{"className":19821},[139,140],[60,19823,19825,19839],{"className":19824},[144],[60,19826,19828],{"className":19827,"style":318},[148],[60,19829,19830,19833],{"style":15878},[60,19831],{"className":19832,"style":325},[156],[60,19834,19836],{"className":19835},[161,162,163,164],[60,19837,814],{"className":19838},[127,164],[60,19840,213],{"className":19841},[212],[60,19843,19845],{"className":19844},[144],[60,19846,19848],{"className":19847,"style":341},[148],[60,19849],{},[60,19851,400],{"className":19852},[131],[60,19854,2152],{"className":19855},[127,178],[60,19857,405],{"className":19858},[267],[26,19860,19861],{},"得证。",[15,19863],{},[18,19865,19867],{"id":19866},"_3-求非齐次方程的通解","3. 求非齐次方程的通解",[23,19869,19870,19871,19873],{},"利用",[26,19872,15731],{},"求解。",[496,19875,19877,19878,19999,20000],{"id":19876},"_1-xxcostx-x-cos-txxcost已知-x1etx2etx_1-et-x_2-e-tx1etx2et","(1) ",[60,19879,19881,19915],{"className":19880},[63],[60,19882,19884],{"className":19883},[67],[69,19885,19886],{"xmlns":71},[73,19887,19888,19912],{},[76,19889,19890,19900,19902,19904,19906,19908,19910],{},[550,19891,19892,19894],{},[84,19893,359],{},[76,19895,19896,19898],{},[397,19897,557],{"mathvariant":86},[397,19899,557],{"mathvariant":86},[397,19901,817],{},[84,19903,359],{},[397,19905,448],{},[84,19907,11088],{},[397,19909,1465],{},[84,19911,2152],{},[106,19913,19914],{"encoding":108},"x'' - x = \\cos t",[60,19916,19918,19966,19984],{"className":19917,"ariaHidden":114},[113],[60,19919,19921,19925,19957,19960,19963],{"className":19920},[118],[60,19922],{"className":19923,"style":19924},[122],"height:0.8352em;vertical-align:-0.0833em;",[60,19926,19928,19931],{"className":19927},[127],[60,19929,359],{"className":19930},[127,178],[60,19932,19934],{"className":19933},[183],[60,19935,19937],{"className":19936},[139],[60,19938,19940],{"className":19939},[144],[60,19941,19943],{"className":19942,"style":605},[148],[60,19944,19945,19948],{"style":608},[60,19946],{"className":19947,"style":325},[156],[60,19949,19951],{"className":19950},[161,162,163,164],[60,19952,19954],{"className":19953},[127,164],[60,19955,17727],{"className":19956},[127,164],[60,19958],{"className":19959,"style":924},[469],[60,19961,817],{"className":19962},[928],[60,19964],{"className":19965,"style":924},[469],[60,19967,19969,19972,19975,19978,19981],{"className":19968},[118],[60,19970],{"className":19971,"style":371},[122],[60,19973,359],{"className":19974},[127,178],[60,19976],{"className":19977,"style":470},[469],[60,19979,448],{"className":19980},[474],[60,19982],{"className":19983,"style":470},[469],[60,19985,19987,19990,19993,19996],{"className":19986},[118],[60,19988],{"className":19989,"style":6002},[122],[60,19991,11088],{"className":19992},[1495],[60,19994],{"className":19995,"style":653},[469],[60,19997,2152],{"className":19998},[127,178],"，已知 ",[60,20001,20003,20049],{"className":20002},[63],[60,20004,20006],{"className":20005},[67],[69,20007,20008],{"xmlns":71},[73,20009,20010,20046],{},[76,20011,20012,20018,20020,20026,20028,20034,20036],{},[96,20013,20014,20016],{},[84,20015,359],{},[102,20017,820],{},[397,20019,448],{},[550,20021,20022,20024],{},[84,20023,981],{},[84,20025,2152],{},[397,20027,569],{"separator":114},[96,20029,20030,20032],{},[84,20031,359],{},[102,20033,814],{},[397,20035,448],{},[550,20037,20038,20040],{},[84,20039,981],{},[76,20041,20042,20044],{},[397,20043,817],{},[84,20045,2152],{},[106,20047,20048],{"encoding":108},"x_1 = e^t, x_2 = e^{-t}",[60,20050,20052,20107,20199],{"className":20051,"ariaHidden":114},[113],[60,20053,20055,20058,20098,20101,20104],{"className":20054},[118],[60,20056],{"className":20057,"style":2734},[122],[60,20059,20061,20064],{"className":20060},[127],[60,20062,359],{"className":20063},[127,178],[60,20065,20067],{"className":20066},[183],[60,20068,20070,20090],{"className":20069},[139,140],[60,20071,20073,20087],{"className":20072},[144],[60,20074,20076],{"className":20075,"style":318},[148],[60,20077,20078,20081],{"style":1940},[60,20079],{"className":20080,"style":325},[156],[60,20082,20084],{"className":20083},[161,162,163,164],[60,20085,820],{"className":20086},[127,164],[60,20088,213],{"className":20089},[212],[60,20091,20093],{"className":20092},[144],[60,20094,20096],{"className":20095,"style":341},[148],[60,20097],{},[60,20099],{"className":20100,"style":470},[469],[60,20102,448],{"className":20103},[474],[60,20105],{"className":20106,"style":470},[469],[60,20108,20110,20114,20144,20147,20150,20190,20193,20196],{"className":20109},[118],[60,20111],{"className":20112,"style":20113},[122],"height:0.988em;vertical-align:-0.1944em;",[60,20115,20117,20120],{"className":20116},[127],[60,20118,981],{"className":20119},[127,178],[60,20121,20123],{"className":20122},[183],[60,20124,20126],{"className":20125},[139],[60,20127,20129],{"className":20128},[144],[60,20130,20133],{"className":20131,"style":20132},[148],"height:0.7936em;",[60,20134,20135,20138],{"style":608},[60,20136],{"className":20137,"style":325},[156],[60,20139,20141],{"className":20140},[161,162,163,164],[60,20142,2152],{"className":20143},[127,178,164],[60,20145,569],{"className":20146},[649],[60,20148],{"className":20149,"style":653},[469],[60,20151,20153,20156],{"className":20152},[127],[60,20154,359],{"className":20155},[127,178],[60,20157,20159],{"className":20158},[183],[60,20160,20162,20182],{"className":20161},[139,140],[60,20163,20165,20179],{"className":20164},[144],[60,20166,20168],{"className":20167,"style":318},[148],[60,20169,20170,20173],{"style":1940},[60,20171],{"className":20172,"style":325},[156],[60,20174,20176],{"className":20175},[161,162,163,164],[60,20177,814],{"className":20178},[127,164],[60,20180,213],{"className":20181},[212],[60,20183,20185],{"className":20184},[144],[60,20186,20188],{"className":20187,"style":341},[148],[60,20189],{},[60,20191],{"className":20192,"style":470},[469],[60,20194,448],{"className":20195},[474],[60,20197],{"className":20198,"style":470},[469],[60,20200,20202,20205],{"className":20201},[118],[60,20203],{"className":20204,"style":20132},[122],[60,20206,20208,20211],{"className":20207},[127],[60,20209,981],{"className":20210},[127,178],[60,20212,20214],{"className":20213},[183],[60,20215,20217],{"className":20216},[139],[60,20218,20220],{"className":20219},[144],[60,20221,20223],{"className":20222,"style":20132},[148],[60,20224,20225,20228],{"style":608},[60,20226],{"className":20227,"style":325},[156],[60,20229,20231],{"className":20230},[161,162,163,164],[60,20232,20234,20237],{"className":20233},[127,164],[60,20235,817],{"className":20236},[127,164],[60,20238,2152],{"className":20239},[127,178,164],[23,20241,20242,20245,20311,20312,488],{},[26,20243,20244],{},"Step 1: 检查系数",[60,20246,20248,20270],{"className":20247},[63],[60,20249,20251],{"className":20250},[67],[69,20252,20253],{"xmlns":71},[73,20254,20255,20267],{},[76,20256,20257],{},[550,20258,20259,20261],{},[84,20260,359],{},[76,20262,20263,20265],{},[397,20264,557],{"mathvariant":86},[397,20266,557],{"mathvariant":86},[106,20268,20269],{"encoding":108},"x''",[60,20271,20273],{"className":20272,"ariaHidden":114},[113],[60,20274,20276,20279],{"className":20275},[118],[60,20277],{"className":20278,"style":605},[122],[60,20280,20282,20285],{"className":20281},[127],[60,20283,359],{"className":20284},[127,178],[60,20286,20288],{"className":20287},[183],[60,20289,20291],{"className":20290},[139],[60,20292,20294],{"className":20293},[144],[60,20295,20297],{"className":20296,"style":605},[148],[60,20298,20299,20302],{"style":608},[60,20300],{"className":20301,"style":325},[156],[60,20303,20305],{"className":20304},[161,162,163,164],[60,20306,20308],{"className":20307},[127,164],[60,20309,17727],{"className":20310},[127,164]," 前面系数是 1，合格。",[60,20313,20315,20343],{"className":20314},[63],[60,20316,20318],{"className":20317},[67],[69,20319,20320],{"xmlns":71},[73,20321,20322,20340],{},[76,20323,20324,20326,20328,20330,20332,20334,20336,20338],{},[84,20325,562],{},[397,20327,400],{"stretchy":399},[84,20329,2152],{},[397,20331,405],{"stretchy":399},[397,20333,448],{},[84,20335,11088],{},[397,20337,1465],{},[84,20339,2152],{},[106,20341,20342],{"encoding":108},"f(t) = \\cos t",[60,20344,20346,20373],{"className":20345,"ariaHidden":114},[113],[60,20347,20349,20352,20355,20358,20361,20364,20367,20370],{"className":20348},[118],[60,20350],{"className":20351,"style":418},[122],[60,20353,562],{"className":20354,"style":639},[127,178],[60,20356,400],{"className":20357},[131],[60,20359,2152],{"className":20360},[127,178],[60,20362,405],{"className":20363},[267],[60,20365],{"className":20366,"style":470},[469],[60,20368,448],{"className":20369},[474],[60,20371],{"className":20372,"style":470},[469],[60,20374,20376,20379,20382,20385],{"className":20375},[118],[60,20377],{"className":20378,"style":6002},[122],[60,20380,11088],{"className":20381},[1495],[60,20383],{"className":20384,"style":653},[469],[60,20386,2152],{"className":20387},[127,178],[23,20389,20390,20393,20394,20551,20552,21834],{},[26,20391,20392],{},"Step 2: 列方程组（常数变易法模板）","\n我们需要求 ",[60,20395,20397,20428],{"className":20396},[63],[60,20398,20400],{"className":20399},[67],[69,20401,20402],{"xmlns":71},[73,20403,20404,20425],{},[76,20405,20406,20415,20417],{},[2127,20407,20408,20411,20413],{},[84,20409,20410],{},"c",[102,20412,820],{},[397,20414,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,20416,569],{"separator":114},[2127,20418,20419,20421,20423],{},[84,20420,20410],{},[102,20422,814],{},[397,20424,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,20426,20427],{"encoding":108},"c_1', 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e^t + c_2' e^{-t} = 0 \\\\\nc_1' (e^t)' + c_2' (e^{-t})' = \\cos t\n\\end{cases}\n\\implies\n\\begin{cases}\nc_1' e^t + c_2' e^{-t} = 0 \\quad \\text{---(1)} \\\\\nc_1' e^t - c_2' e^{-t} = \\cos t \\quad \\text{---(2)}\n\\end{cases}",[60,20811,20813,21361],{"className":20812,"ariaHidden":114},[113],[60,20814,20816,20820,21346,21349,21352,21355,21358],{"className":20815},[118],[60,20817],{"className":20818,"style":20819},[122],"height:3em;vertical-align:-1.25em;",[60,20821,20823,20830,21343],{"className":20822},[2326],[60,20824,20826],{"className":20825,"style":2331},[131,2330],[60,20827,20568],{"className":20828},[2335,20829],"size4",[60,20831,20833],{"className":20832},[127],[60,20834,20836],{"className":20835},[20570],[60,20837,20840],{"className":20838},[20839],"col-align-l",[60,20841,20843,21334],{"className":20842},[139,140],[60,20844,20846,21331],{"className":20845},[144],[60,20847,20850,21053],{"className":20848,"style":20849},[148],"height:1.69em;",[60,20851,20853,20857],{"style":20852},"top:-3.69em;",[60,20854],{"className":20855,"style":20856},[156],"height:3.008em;",[60,20858,20860,20914,20943,20946,20949,20952,21006,21041,21044,21047,21050],{"className":20859},[127],[60,20861,20863,20866],{"className":20862},[127],[60,20864,20410],{"className":20865},[127,178],[60,20867,20869],{"className":20868},[183],[60,20870,20872,20906],{"className":20871},[139,140],[60,20873,20875,20903],{"className":20874},[144],[60,20876,20878,20889],{"className":20877,"style":605},[148],[60,20879,20880,20883],{"style":17413},[60,20881],{"className":20882,"style":325},[156],[60,20884,20886],{"className":20885},[161,162,163,164],[60,20887,820],{"className":20888},[127,164],[60,20890,20891,20894],{"style":608},[60,20892],{"className":20893,"style":325},[156],[60,20895,20897],{"className":20896},[161,162,163,164],[60,20898,20900],{"className":20899},[127,164],[60,20901,557],{"className":20902},[127,164],[60,20904,213],{"className":20905},[212],[60,20907,20909],{"className":20908},[144],[60,20910,20912],{"className":20911,"style":17446},[148],[60,20913],{},[60,20915,20917,20920],{"className":20916},[127],[60,20918,981],{"className":20919},[127,178],[60,20921,20923],{"className":20922},[183],[60,20924,20926],{"className":20925},[139],[60,20927,20929],{"className":20928},[144],[60,20930,20932],{"className":20931,"style":20132},[148],[60,20933,20934,20937],{"style":608},[60,20935],{"className":20936,"style":325},[156],[60,20938,20940],{"className":20939},[161,162,163,164],[60,20941,2152],{"className":20942},[127,178,164],[60,20944],{"className":20945,"style":924},[469],[60,20947,990],{"className":20948},[928],[60,20950],{"className":20951,"style":924},[469],[60,20953,20955,20958],{"className":20954},[127],[60,20956,20410],{"className":20957},[127,178],[60,20959,20961],{"className":20960},[183],[60,20962,20964,20998],{"className":20963},[139,140],[60,20965,20967,20995],{"className":20966},[144],[60,20968,20970,20981],{"className":20969,"style":605},[148],[60,20971,20972,20975],{"style":17413},[60,20973],{"className":20974,"style":325},[156],[60,20976,20978],{"className":20977},[161,162,163,164],[60,20979,814],{"className":20980},[127,164],[60,20982,20983,20986],{"style":608},[60,20984],{"className":20985,"style":325},[156],[60,20987,20989],{"className":20988},[161,162,163,164],[60,20990,20992],{"className":20991},[127,164],[60,20993,557],{"className":20994},[127,164],[60,20996,213],{"className":20997},[212],[60,20999,21001],{"className":21000},[144],[60,21002,21004],{"className":21003,"style":17446},[148],[60,21005],{},[60,21007,21009,21012],{"className":21008},[127],[60,21010,981],{"className":21011},[127,178],[60,21013,21015],{"className":21014},[183],[60,21016,21018],{"className":21017},[139],[60,21019,21021],{"className":21020},[144],[60,21022,21024],{"className":21023,"style":20132},[148],[60,21025,21026,21029],{"style":608},[60,21027],{"className":21028,"style":325},[156],[60,21030,21032],{"className":21031},[161,162,163,164],[60,21033,21035,21038],{"className":21034},[127,164],[60,21036,817],{"className":21037},[127,164],[60,21039,2152],{"className":21040},[127,178,164],[60,21042],{"className":21043,"style":470},[469],[60,21045,448],{"className":21046},[474],[60,21048],{"className":21049,"style":470},[469],[60,21051,104],{"className":21052},[127],[60,21054,21056,21059],{"style":21055},"top:-2.25em;",[60,21057],{"className":21058,"style":20856},[156],[60,21060,21062,21116,21119,21148,21180,21183,21186,21189,21243,21246,21281,21313,21316,21319,21322,21325,21328],{"className":21061},[127],[60,21063,21065,21068],{"className":21064},[127],[60,21066,20410],{"className":21067},[127,178],[60,21069,21071],{"className":21070},[183],[60,21072,21074,21108],{"className":21073},[139,140],[60,21075,21077,21105],{"className":21076},[144],[60,21078,21080,21091],{"className":21079,"style":605},[148],[60,21081,21082,21085],{"style":17413},[60,21083],{"className":21084,"style":325},[156],[60,21086,21088],{"className":21087},[161,162,163,164],[60,21089,820],{"className":21090},[127,164],[60,21092,21093,21096],{"style":608},[60,21094],{"className":21095,"style":325},[156],[60,21097,21099],{"className":21098},[161,162,163,164],[60,21100,21102],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assName":21410},[183],[60,21412,21414,21448],{"className":21413},[139,140],[60,21415,21417,21445],{"className":21416},[144],[60,21418,21420,21431],{"className":21419,"style":605},[148],[60,21421,21422,21425],{"style":17413},[60,21423],{"className":21424,"style":325},[156],[60,21426,21428],{"className":21427},[161,162,163,164],[60,21429,820],{"className":21430},[127,164],[60,21432,21433,21436],{"style":608},[60,21434],{"className":21435,"style":325},[156],[60,21437,21439],{"className":21438},[161,162,163,164],[60,21440,21442],{"className":21441},[127,164],[60,21443,557],{"className":21444},[127,164],[60,21446,213],{"className":21447},[212],[60,21449,21451],{"className":21450},[144],[60,21452,21454],{"className":21453,"style":17446},[148],[60,21455],{},[60,21457,21459,21462],{"className":21458},[127],[60,21460,981],{"className":21461},[127,178],[60,21463,21465],{"className":21464},[183],[60,21466,21468],{"className":21467},[139],[60,21469,21471],{"className":21470},[144],[60,21472,21474],{"className":21473,"style":20132},[148],[60,21475,21476,21479],{"style":608},[60,21477],{"className":21478,"style":325},[156],[60,21480,21482],{"className":21481},[161,162,163,164],[60,21483,2152],{"className":21484},[127,178,164],[60,21486],{"className":21487,"style":924},[469],[60,21489,990],{"className":21490},[928],[60,21492],{"className":21493,"style":924},[469],[60,21495,21497,21500],{"className":21496},[127],[60,21498,20410],{"className":21499},[127,178],[60,21501,21503],{"className":21502},[183],[60,21504,21506,21540],{"className":21505},[139,140],[60,21507,21509,21537],{"className":21508},[144],[60,21510,21512,21523],{"className":21511,"style":605},[148],[60,21513,21514,21517],{"style":17413},[60,21515],{"className":21516,"style":325},[156],[60,21518,21520],{"className":21519},[161,162,163,164],[60,21521,814],{"className":21522},[127,164],[60,21524,21525,21528],{"style":608},[60,21526],{"className":21527,"style":325},[156],[60,21529,21531],{"className":21530},[161,162,163,164],[60,21532,21534],{"className":21533},[127,164],[60,21535,557],{"className":21536},[127,164],[60,21538,213],{"className":21539},[212],[60,21541,21543],{"className":21542},[144],[60,21544,21546],{"className":21545,"style":17446},[148],[60,21547],{},[60,21549,21551,21554],{"className":21550},[127],[60,21552,981],{"className":21553},[127,178],[60,21555,21557],{"className":21556},[183],[60,21558,21560],{"className":21559},[139],[60,21561,21563],{"className":21562},[144],[60,21564,21566],{"className":21565,"style":20132},[148],[60,21567,21568,21571],{"style":608},[60,21569],{"className":21570,"style":325},[156],[60,21572,21574],{"className":21573},[161,162,163,164],[60,21575,21577,21580],{"className":21576},[127,164],[60,21578,817],{"className":21579},[127,164],[60,21581,2152],{"className":21582},[127,178,164],[60,21584],{"className":21585,"style":470},[469],[60,21587,448],{"className":21588},[474],[60,21590],{"className":21591,"style":470},[469],[60,21593,104],{"className":21594},[127],[60,21596],{"className":21597,"style":13455},[469],[60,21599,21601],{"className":21600},[127,13462],[60,21602,20751],{"className":21603},[127],[60,21605,21606,21609],{"style":21055},[60,21607],{"className":21608,"style":20856},[156],[60,21610,21612,21666,21695,21698,21701,21704,21758,21793,21796,21799,21802,21805,21808,21811,21814],{"className":21611},[127],[60,21613,21615,21618],{"className":21614},[127],[60,21616,20410],{"className":21617},[127,178],[60,21619,21621],{"className":21620},[183],[60,21622,21624,21658],{"className":21623},[139,140],[60,21625,21627,21655],{"className":21626},[144],[60,21628,21630,21641],{"className":21629,"style":605},[148],[60,21631,21632,21635],{"style":17413},[60,21633],{"className":21634,"style":325},[156],[60,21636,21638],{"className":21637},[161,162,163,164],[60,21639,820],{"className":21640},[127,164],[60,21642,21643,21646],{"style":608},[60,21644],{"className":21645,"style":325},[156],[60,21647,21649],{"className":21648},[161,162,163,164],[60,21650,21652],{"className":21651},[127,164],[60,21653,557],{"className":21654},[127,164],[60,21656,213],{"className":21657},[212],[60,21659,21661],{"className":21660},[144],[60,21662,21664],{"className":21663,"style":17446},[148],[60,21665],{},[60,21667,21669,21672],{"className":21668},[127],[60,21670,981],{"className":21671},[127,178],[60,21673,21675],{"className":21674},[183],[60,21676,21678],{"className":21677},[139],[60,21679,21681],{"className":21680},[144],[60,21682,21684],{"className":21683,"style":20132},[148],[60,21685,21686,21689],{"style":608},[60,21687],{"className":21688,"style":325},[156],[60,21690,21692],{"className":21691},[161,162,163,164],[60,21693,2152],{"className":21694},[127,178,164],[60,21696],{"className":21697,"style":924},[469],[60,21699,817],{"className":21700},[928],[60,21702],{"className":21703,"style":924},[469],[60,21705,21707,21710],{"className":21706},[127],[60,21708,20410],{"className":21709},[127,178],[60,21711,21713],{"className":21712},[183],[60,21714,21716,21750],{"className":21715},[139,140],[60,21717,21719,21747],{"className":21718},[144],[60,21720,21722,21733],{"className":21721,"style":605},[148],[60,21723,21724,21727],{"style":17413},[60,21725],{"className":21726,"style":325},[156],[60,21728,21730],{"className":21729},[161,162,163,164],[60,21731,814],{"className":21732},[127,164],[60,21734,21735,21738],{"style":608},[60,21736],{"className":21737,"style":325},[156],[60,21739,21741],{"className":21740},[161,162,163,164],[60,21742,21744],{"className":21743},[127,164],[60,21745,557],{"className":21746},[127,164],[60,21748,213],{"className":21749},[212],[60,21751,21753],{"className":21752},[144],[60,21754,21756],{"className":21755,"style":17446},[148],[60,21757],{},[60,21759,21761,21764],{"className":21760},[127],[60,21762,981],{"className":21763},[127,178],[60,21765,21767],{"className":21766},[183],[60,21768,21770],{"className":21769},[139],[60,21771,21773],{"className":21772},[144],[60,21774,21776],{"className":21775,"style":20132},[148],[60,21777,21778,21781],{"style":608},[60,21779],{"className":21780,"style":325},[156],[60,21782,21784],{"className":21783},[161,162,163,164],[60,21785,21787,21790],{"className":21786},[127,164],[60,21788,817],{"className":21789},[127,164],[60,21791,2152],{"className":21792},[127,178,164],[60,21794],{"className":21795,"style":470},[469],[60,21797,448],{"className":21798},[474],[60,21800],{"className":21801,"style":470},[469],[60,21803,11088],{"className":21804},[1495],[60,21806],{"className":21807,"style":653},[469],[60,21809,2152],{"className":21810},[127,178],[60,21812],{"className":21813,"style":13455},[469],[60,21815,21817],{"className":21816},[127,13462],[60,21818,20806],{"className":21819},[127],[60,21821,213],{"className":21822},[212],[60,21824,21826],{"className":21825},[144],[60,21827,21829],{"className":21828,"style":21340},[148],[60,21830],{},[60,21832],{"className":21833},[267,132],"\n]",[23,21836,21837,21840,21841,22244,22245],{},[26,21838,21839],{},"Step 3: 解方程组","\n(1) + (2) 得：",[60,21842,21844,21918],{"className":21843},[63],[60,21845,21847],{"className":21846},[67],[69,21848,21849],{"xmlns":71},[73,21850,21851,21915],{},[76,21852,21853,21855,21863,21869,21871,21873,21875,21877,21879,21881,21883,21891,21893,21899,21909,21911,21913],{},[102,21854,814],{},[2127,21856,21857,21859,21861],{},[84,21858,20410],{},[102,21860,820],{},[397,21862,557],{"mathvariant":86,"lspace":556,"rspace":556},[550,21864,21865,21867],{},[84,21866,981],{},[84,21868,2152],{},[397,21870,448],{},[84,21872,11088],{},[397,21874,1465],{},[84,21876,2152],{},[13095,21878,18294],{},[397,21880,18297],{},[13095,21882,18294],{},[2127,21884,21885,21887,21889],{},[84,21886,20410],{},[102,21888,820],{},[397,21890,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,21892,448],{},[79,21894,21895,21897],{},[102,21896,820],{},[102,21898,814],{},[550,21900,21901,21903],{},[84,21902,981],{},[76,21904,21905,21907],{},[397,21906,817],{},[84,21908,2152],{},[84,21910,11088],{},[397,21912,1465],{},[84,21914,2152],{},[106,21916,21917],{"encoding":108},"2c_1' e^t = \\cos t \\implies c_1' = \\frac{1}{2}e^{-t}\\cos t",[60,21919,21921,22023,22054,22123],{"className":21920,"ariaHidden":114},[113],[60,21922,21924,21928,21931,21985,22014,22017,22020],{"className":21923},[118],[60,21925],{"className":21926,"style":21927},[122],"height:1.0417em;vertical-align:-0.2481em;",[60,21929,814],{"className":21930},[127],[60,21932,21934,21937],{"className":21933},[127],[60,21935,20410],{"className":21936},[127,178],[60,21938,21940],{"className":21939},[183],[60,21941,21943,21977],{"className":21942},[139,140],[60,21944,21946,21974],{"className":21945},[144],[60,21947,21949,21960],{"className":21948,"style":605},[148],[60,21950,21951,21954],{"style":17413},[60,21952],{"className":21953,"style":325},[156],[60,21955,21957],{"className":21956},[161,162,163,164],[60,21958,820],{"className":21959},[127,164],[60,21961,21962,21965],{"style":608},[60,21963],{"className":21964,"style":325},[156],[60,21966,21968],{"className":21967},[161,162,163,164],[60,21969,21971],{"className":21970},[127,164],[60,21972,557],{"className":21973},[127,164],[60,21975,213],{"className":21976},[212],[60,21978,21980],{"className":21979},[144],[60,21981,21983],{"className":21982,"style":17446},[148],[60,21984],{},[60,21986,21988,21991],{"className":21987},[127],[60,21989,981],{"className":21990},[127,178],[60,21992,21994],{"className":21993},[183],[60,21995,21997],{"className":21996},[139],[60,21998,22000],{"className":21999},[144],[60,22001,22003],{"className":22002,"style":20132},[148],[60,22004,22005,22008],{"style":608},[60,22006],{"className":22007,"style":325},[156],[60,22009,22011],{"className":22010},[161,162,163,164],[60,22012,2152],{"className":22013},[127,178,164],[60,22015],{"className":22016,"style":470},[469],[60,22018,448],{"className":22019},[474],[60,22021],{"className":22022,"style":470},[469],[60,22024,22026,22030,22033,22036,22039,22042,22045,22048,22051],{"className":22025},[118],[60,22027],{"className":22028,"style":22029},[122],"height:0.6391em;vertical-align:-0.024em;",[60,22031,11088],{"className":22032},[1495],[60,22034],{"className":22035,"style":653},[469],[60,22037,2152],{"className":22038},[127,178],[60,22040],{"className":22041,"style":470},[469],[60,22043],{"className":22044,"style":470},[469],[60,22046,18297],{"className":22047},[474],[60,22049],{"className":22050,"style":470},[469],[60,22052],{"className":22053,"style":470},[469],[60,22055,22057,22060,22114,22117,22120],{"className":22056},[118],[60,22058],{"className":22059,"style":17392},[122],[60,22061,22063,22066],{"className":22062},[127],[60,22064,20410],{"className":22065},[127,178],[60,22067,22069],{"className":22068},[183],[60,22070,22072,22106],{"className":22071},[139,140],[60,22073,22075,22103],{"className":22074},[144],[60,22076,22078,22089],{"className":22077,"style":605},[148],[60,22079,22080,22083],{"style":17413},[60,22081],{"className":22082,"style":325},[156],[60,22084,22086],{"className":22085},[161,162,163,164],[60,22087,820],{"className":22088},[127,164],[60,22090,22091,22094],{"style":608},[60,22092],{"className":22093,"style":325},[156],[60,22095,22097],{"className":22096},[161,162,163,164],[60,22098,22100],{"className":22099},[127,164],[60,22101,557],{"className":22102},[127,164],[60,22104,213],{"className":22105},[212],[60,22107,22109],{"className":22108},[144],[60,22110,22112],{"className":22111,"style":17446},[148],[60,22113],{},[60,22115],{"className":22116,"style":470},[469],[60,22118,448],{"className":22119},[474],[60,22121],{"className":22122,"style":470},[469],[60,22124,22126,22129,22197,22232,22235,22238,22241],{"className":22125},[118],[60,22127],{"className":22128,"style":12028},[122],[60,22130,22132,22135,22194],{"className":22131},[127],[60,22133],{"className":22134},[131,132],[60,22136,22138],{"className":22137},[79],[60,22139,22141,22186],{"className":22140},[139,140],[60,22142,22144,22183],{"className":22143},[144],[60,22145,22147,22161,22169],{"className":22146,"style":11547},[148],[60,22148,22149,22152],{"style":152},[60,22150],{"className":22151,"style":157},[156],[60,22153,22155],{"className":22154},[161,162,163,164],[60,22156,22158],{"className":22157},[127,164],[60,22159,814],{"className":22160},[127,164],[60,22162,22163,22166],{"style":225},[60,22164],{"className":22165,"style":157},[156],[60,22167],{"className":22168,"style":233},[232],[60,22170,22171,22174],{"style":1105},[60,22172],{"className":22173,"style":157},[156],[60,22175,22177],{"className":22176},[161,162,163,164],[60,22178,22180],{"className":22179},[127,164],[60,22181,820],{"className":22182},[127,164],[60,22184,213],{"className":22185},[212],[60,22187,22189],{"className":22188},[144],[60,22190,22192],{"className":22191,"style":3907},[148],[60,22193],{},[60,22195],{"className":22196},[267,132],[60,22198,22200,22203],{"className":22199},[127],[60,22201,981],{"className":22202},[127,178],[60,22204,22206],{"className":22205},[183],[60,22207,22209],{"className":22208},[139],[60,22210,22212],{"className":22211},[144],[60,22213,22215],{"className":22214,"style":20132},[148],[60,22216,22217,22220],{"style":608},[60,22218],{"className":22219,"style":325},[156],[60,22221,22223],{"className":22222},[161,162,163,164],[60,22224,22226,22229],{"className":22225},[127,164],[60,22227,817],{"className":22228},[127,164],[60,22230,2152],{"className":22231},[127,178,164],[60,22233],{"className":22234,"style":653},[469],[60,22236,11088],{"className":22237},[1495],[60,22239],{"className":22240,"style":653},[469],[60,22242,2152],{"className":22243},[127,178],"\n(1) - (2) 得：",[60,22246,22248,22326],{"className":22247},[63],[60,22249,22251],{"className":22250},[67],[69,22252,22253],{"xmlns":71},[73,22254,22255,22323],{},[76,22256,22257,22259,22267,22277,22279,22281,22283,22285,22287,22289,22291,22293,22301,22303,22305,22311,22317,22319,22321],{},[102,22258,814],{},[2127,22260,22261,22263,22265],{},[84,22262,20410],{},[102,22264,814],{},[397,22266,557],{"mathvariant":86,"lspace":556,"rspace":556},[550,22268,22269,22271],{},[84,22270,981],{},[76,22272,22273,22275],{},[397,22274,817],{},[84,22276,2152],{},[397,22278,448],{},[397,22280,817],{},[84,22282,11088],{},[397,22284,1465],{},[84,22286,2152],{},[13095,22288,18294],{},[397,22290,18297],{},[13095,22292,18294],{},[2127,22294,22295,22297,22299],{},[84,22296,20410],{},[102,22298,814],{},[397,22300,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,22302,448],{},[397,22304,817],{},[79,22306,22307,22309],{},[102,22308,820],{},[102,22310,814],{},[550,22312,22313,22315],{},[84,22314,981],{},[84,22316,2152],{},[84,22318,11088],{},[397,22320,1465],{},[84,22322,2152],{},[106,22324,22325],{"encoding":108},"2c_2' e^{-t} = -\\cos t \\implies c_2' = -\\frac{1}{2}e^t\\cos t",[60,22327,22329,22436,22473,22542],{"className":22328,"ariaHidden":114},[113],[60,22330,22332,22335,22338,22392,22427,22430,22433],{"className":22331},[118],[60,22333],{"className":22334,"style":21927},[122],[60,22336,814],{"className":22337},[127],[60,22339,22341,22344],{"className":22340},[127],[60,22342,20410],{"className":22343},[127,178],[60,22345,22347],{"className":22346},[183],[60,22348,22350,22384],{"className":22349},[139,140],[60,22351,22353,22381],{"className":22352},[144],[60,22354,22356,22367],{"className":22355,"style":605},[148],[60,22357,22358,22361],{"style":17413},[60,22359],{"className":22360,"style":325},[156],[60,22362,22364],{"className":22363},[161,162,163,164],[60,22365,814],{"className":22366},[127,164],[60,22368,22369,22372],{"style":608},[60,22370],{"className":22371,"style":325},[156],[60,22373,22375],{"className":22374},[161,162,163,164],[60,22376,22378],{"className":22377},[127,164],[60,22379,557],{"className":22380},[127,164],[60,22382,213],{"className":22383},[212],[60,22385,22387],{"className":22386},[144],[60,22388,22390],{"className":22389,"style":17446},[148],[60,22391],{},[60,22393,22395,22398],{"className":22394},[127],[60,22396,981],{"className":22397},[127,178],[60,22399,22401],{"className":22400},[183],[60,22402,22404],{"className":22403},[139],[60,22405,22407],{"className":22406},[144],[60,22408,22410],{"className":22409,"style":20132},[148],[60,22411,22412,22415],{"style":608},[60,22413],{"className":22414,"style":325},[156],[60,22416,22418],{"className":22417},[161,162,163,164],[60,22419,22421,22424],{"className":22420},[127,164],[60,22422,817],{"className":22423},[127,164],[60,22425,2152],{"className":22426},[127,178,164],[60,22428],{"className":22429,"style":470},[469],[60,22431,448],{"className":22432},[474],[60,22434],{"className":22435,"style":470},[469],[60,22437,22439,22443,22446,22449,22452,22455,22458,22461,22464,22467,22470],{"className":22438},[118],[60,22440],{"className":22441,"style":22442},[122],"height:0.6984em;vertical-align:-0.0833em;",[60,22444,817],{"className":22445},[127],[60,22447],{"className":22448,"style":653},[469],[60,22450,11088],{"className":22451},[1495],[60,22453],{"className":22454,"style":653},[469],[60,22456,2152],{"className":22457},[127,178],[60,22459],{"className":22460,"style":470},[469],[60,22462],{"className":22463,"style":470},[469],[60,22465,18297],{"className":22466},[474],[60,22468],{"className":22469,"style":470},[469],[60,22471],{"className":22472,"style":470},[469],[60,22474,22476,22479,22533,22536,22539],{"className":22475},[118],[60,22477],{"className":22478,"style":17392},[122],[60,22480,22482,22485],{"className":22481},[127],[60,22483,20410],{"className":22484},[127,178],[60,22486,22488],{"className":22487},[183],[60,22489,22491,22525],{"className":22490},[139,140],[60,22492,22494,22522],{"className":22493},[144],[60,22495,22497,22508],{"className":22496,"style":605},[148],[60,22498,22499,22502],{"style":17413},[60,22500],{"className":22501,"style":325},[156],[60,22503,22505],{"className":22504},[161,162,163,164],[60,22506,814],{"className":22507},[127,164],[60,22509,22510,22513],{"style":608},[60,22511],{"className":22512,"style":325},[156],[60,22514,22516],{"className":22515},[161,162,163,164],[60,22517,22519],{"className":22518},[127,164],[60,22520,557],{"className":22521},[127,164],[60,22523,213],{"className":22524},[212],[60,22526,22528],{"className":22527},[144],[60,22529,22531],{"className":22530,"style":17446},[148],[60,22532],{},[60,22534],{"className":22535,"style":470},[469],[60,22537,448],{"className":22538},[474],[60,22540],{"className":22541,"style":470},[469],[60,22543,22545,22548,22551,22619,22648,22651,22654,22657],{"className":22544},[118],[60,22546],{"className":22547,"style":12028},[122],[60,22549,817],{"className":22550},[127],[60,22552,22554,22557,22616],{"className":22553},[127],[60,22555],{"className":22556},[131,132],[60,22558,22560],{"className":22559},[79],[60,22561,22563,22608],{"className":22562},[139,140],[60,22564,22566,22605],{"className":22565},[144],[60,22567,22569,22583,22591],{"className":22568,"style":11547},[148],[60,22570,22571,22574],{"style":152},[60,22572],{"className":22573,"style":157},[156],[60,22575,22577],{"className":22576},[161,162,163,164],[60,22578,22580],{"className":22579},[127,164],[60,22581,814],{"className":22582},[127,164],[60,22584,22585,22588],{"style":225},[60,22586],{"className":22587,"style":157},[156],[60,22589],{"className":22590,"style":233},[232],[60,22592,22593,22596],{"style":1105},[60,22594],{"className":22595,"style":157},[156],[60,22597,22599],{"className":22598},[161,162,163,164],[60,22600,22602],{"className":22601},[127,164],[60,22603,820],{"className":22604},[127,164],[60,22606,213],{"className":22607},[212],[60,22609,22611],{"className":22610},[144],[60,22612,22614],{"className":22613,"style":3907},[148],[60,22615],{},[60,22617],{"className":22618},[267,132],[60,22620,22622,22625],{"className":22621},[127],[60,22623,981],{"className":22624},[127,178],[60,22626,22628],{"className":22627},[183],[60,22629,22631],{"className":22630},[139],[60,22632,22634],{"className":22633},[144],[60,22635,22637],{"className":22636,"style":20132},[148],[60,22638,22639,22642],{"style":608},[60,22640],{"className":22641,"style":325},[156],[60,22643,22645],{"className":22644},[161,162,163,164],[60,22646,2152],{"className":22647},[127,178,164],[60,22649],{"className":22650,"style":653},[469],[60,22652,11088],{"className":22653},[1495],[60,22655],{"className":22656,"style":653},[469],[60,22658,2152],{"className":22659},[127,178],[23,22661,22662,22665,22666,22771,22772,23032],{},[26,22663,22664],{},"Step 4: 积分（这里考微积分基本功）","\n这两个积分需要用到“分部积分法”或者“欧拉公式”。\n（注：",[60,22667,22669,22703],{"className":22668},[63],[60,22670,22672],{"className":22671},[67],[69,22673,22674],{"xmlns":71},[73,22675,22676,22700],{},[76,22677,22678,22680,22690,22692,22694,22696,22698],{},[397,22679,2131],{},[550,22681,22682,22684],{},[84,22683,981],{},[76,22685,22686,22688],{},[84,22687,16644],{},[84,22689,2152],{},[84,22691,11088],{},[397,22693,1465],{},[84,22695,2152],{},[84,22697,2173],{},[84,22699,2152],{},[106,22701,22702],{"encoding":108},"\\int e^{at}\\cos t dt",[60,22704,22706],{"className":22705,"ariaHidden":114},[113],[60,22707,22709,22712,22715,22718,22753,22756,22759,22762,22765,22768],{"className":22708},[118],[60,22710],{"className":22711,"style":15487},[122],[60,22713,2131],{"className":22714,"style":2345},[1495,2343,2344],[60,22716],{"className":22717,"style":653},[469],[60,22719,22721,22724],{"className":22720},[127],[60,22722,981],{"className":22723},[127,178],[60,22725,22727],{"className":22726},[183],[60,22728,22730],{"className":22729},[139],[60,22731,22733],{"className":22732},[144],[60,22734,22736],{"className":22735,"style":20132},[148],[60,22737,22738,22741],{"style":608},[60,22739],{"className":22740,"style":325},[156],[60,22742,22744],{"className":22743},[161,162,163,164],[60,22745,22747,22750],{"className":22746},[127,164],[60,22748,16644],{"className":22749},[127,178,164],[60,22751,2152],{"className":22752},[127,178,164],[60,22754],{"className":22755,"style":653},[469],[60,22757,11088],{"className":22758},[1495],[60,22760],{"className":22761,"style":653},[469],[60,22763,2152],{"className":22764},[127,178],[60,22766,2173],{"className":22767},[127,178],[60,22769,2152],{"className":22770},[127,178]," 是经典循环积分，公式为 ",[60,22773,22775,22833],{"className":22774},[63],[60,22776,22778],{"className":22777},[67],[69,22779,22780],{"xmlns":71},[73,22781,22782,22830],{},[76,22783,22784],{},[79,22785,22786,22818],{},[76,22787,22788,22798,22800,22802,22804,22806,22808,22810,22812,22814,22816],{},[550,22789,22790,22792],{},[84,22791,981],{},[76,22793,22794,22796],{},[84,22795,16644],{},[84,22797,2152],{},[397,22799,400],{"stretchy":399},[84,22801,16644],{},[84,22803,11088],{},[397,22805,1465],{},[84,22807,2152],{},[397,22809,990],{},[84,22811,9061],{},[397,22813,1465],{},[84,22815,2152],{},[397,22817,405],{"stretchy":399},[76,22819,22820,22826,22828],{},[550,22821,22822,22824],{},[84,22823,16644],{},[102,22825,814],{},[397,22827,990],{},[102,22829,820],{},[106,22831,22832],{"encoding":108},"\\frac{e^{at}(a\\cos t + \\sin 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= \\frac{1}{2} \\int e^{-t}\\cos t \\, dt = \\frac{1}{2} \\left[ \\frac{e^{-t}(-\\cos t + \\sin t)}{2} \\right] = \\frac{1}{4}e^{-t}(\\sin t - \\cos 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= -\\frac{1}{2} \\int e^t\\cos t \\, dt = -\\frac{1}{2} \\left[ \\frac{e^t(\\cos t + \\sin t)}{2} \\right] = -\\frac{1}{4}e^t(\\sin t + \\cos 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},[131,132],[60,24215,24217],{"className":24216},[79],[60,24218,24220,24336],{"className":24219},[139,140],[60,24221,24223,24333],{"className":24222},[144],[60,24224,24226,24240,24248],{"className":24225,"style":22861},[148],[60,24227,24228,24231],{"style":152},[60,24229],{"className":24230,"style":157},[156],[60,24232,24234],{"className":24233},[161,162,163,164],[60,24235,24237],{"className":24236},[127,164],[60,24238,814],{"className":24239},[127,164],[60,24241,24242,24245],{"style":225},[60,24243],{"className":24244,"style":157},[156],[60,24246],{"className":24247,"style":233},[232],[60,24249,24250,24253],{"style":2485},[60,24251],{"className":24252,"style":157},[156],[60,24254,24256],{"className":24255},[161,162,163,164],[60,24257,24259,24288,24291,24303,24306,24309,24312,24324,24327,24330],{"className":24258},[127,164],[60,24260,24262,24265],{"className":24261},[127,164],[60,24263,981],{"className":24264},[127,178,164],[60,24266,24268],{"className":24267},[183],[60,24269,24271],{"className":24270},[139],[60,24272,24274],{"className":24273},[144],[60,24275,24277],{"className":24276,"style":22945},[148],[60,24278,24279,24282],{"style":1142},[60,24280],{"className":24281,"style":200},[156],[60,24283,24285],{"className":24284},[161,204,205,164],[60,24286,2152],{"className":24287},[127,178,164],[60,24289,400],{"className":24290},[131,164],[60,24292,24294,24297,24300],{"className":24293},[1495,164],[60,24295,20410],{"className":24296},[164],[60,24298,22982],{"className":24299},[164],[60,24301,22986],{"className":24302},[164],[60,24304],{"className":24305,"style":22972},[469,164],[60,24307,2152],{"className":24308},[127,178,164],[60,24310,990],{"className":24311},[928,164],[60,24313,24315,24318,24321],{"className":24314},[1495,164],[60,24316,22986],{"className":24317},[164],[60,24319,23005],{"className":24320},[164],[60,24322,16342],{"className":24323},[164],[60,24325],{"className":24326,"style":22972},[469,164],[60,24328,2152],{"className":24329},[127,178,164],[60,24331,405],{"className":24332},[267,164],[60,24334,213],{"className":24335},[212],[60,24337,24339],{"className":24338},[144],[60,24340,24342],{"className":24341,"style":3907},[148],[60,24343],{},[60,24345],{"className":24346},[267,132],[60,24348,24350],{"className":24349,"style":2331},[267,2330],[60,24351,5004],{"className":24352},[2335,2336],[60,24354],{"className":24355,"style":470},[469],[60,24357,448],{"className":24358},[474],[60,24360],{"className":24361,"style":470},[469],[60,24363,24365,24368,24371,24439,24468,24471,24474,24477,24480,24483,24486],{"className":24364},[118],[60,24366],{"className":24367,"style":12028},[122],[60,24369,817],{"className":24370},[127],[60,24372,24374,24377,24436],{"className":24373},[127],[60,24375],{"className":24376},[131,132],[60,24378,24380],{"className":24379},[79],[60,24381,24383,24428],{"className":24382},[139,140],[60,24384,24386,24425],{"className":24385},[144],[60,24387,24389,24403,24411],{"className":24388,"style":11547},[148],[60,24390,24391,24394],{"style":152},[60,24392],{"className":24393,"style":157},[156],[60,24395,24397],{"className":24396},[161,162,163,164],[60,24398,24400],{"className":24399},[127,164],[60,24401,23145],{"className":24402},[127,164],[60,24404,24405,24408],{"style":225},[60,24406],{"className":24407,"style":157},[156],[60,24409],{"className":24410,"style":233},[232],[60,24412,24413,24416],{"style":1105},[60,24414],{"className":24415,"style":157},[156],[60,24417,24419],{"className":24418},[161,162,163,164],[60,24420,24422],{"className":24421},[127,164],[60,24423,820],{"className":24424},[127,164],[60,24426,213],{"className":24427},[212],[60,24429,24431],{"className":24430},[144],[60,24432,24434],{"className":24433,"style":3907},[148],[60,24435],{},[60,24437],{"className":24438},[267,132],[60,24440,24442,24445],{"className":24441},[127],[60,24443,981],{"className":24444},[127,178],[60,24446,24448],{"className":24447},[183],[60,24449,24451],{"className":24450},[139],[60,24452,24454],{"className":24453},[144],[60,24455,24457],{"className":24456,"style":20132},[148],[60,24458,24459,24462],{"style":608},[60,24460],{"className":24461,"style":325},[156],[60,24463,24465],{"className":24464},[161,162,163,164],[60,24466,2152],{"className":24467},[127,178,164],[60,24469,400],{"className":24470},[131],[60,24472,9061],{"className":24473},[1495],[60,24475],{"className":24476,"style":653},[469],[60,24478,2152],{"className":24479},[127,178],[60,24481],{"className":24482,"style":924},[469],[60,24484,990],{"className":24485},[928],[60,24487],{"className":24488,"style":924},[469],[60,24490,24492,24495,24498,24501,24504],{"className":24491},[118],[60,24493],{"className":24494,"style":418},[122],[60,24496,11088],{"className":24497},[1495],[60,24499],{"className":24500,"style":653},[469],[60,24502,2152],{"className":24503},[127,178],[60,24505,405],{"className":24506},[267],[23,24508,24509,24512,24513,24980,24981,25234,25502,25503],{},[26,24510,24511],{},"Step 5: 写通解","\n通解 ",[60,24514,24516,24595],{"className":24515},[63],[60,24517,24519],{"className":24518},[67],[69,24520,24521],{"xmlns":71},[73,24522,24523,24592],{},[76,24524,24525,24527,24529,24536,24542,24544,24550,24560,24562,24564,24570,24576,24578,24584,24590],{},[84,24526,359],{},[397,24528,448],{},[96,24530,24531,24534],{},[84,24532,24533],{},"C",[102,24535,820],{},[550,24537,24538,24540],{},[84,24539,981],{},[84,24541,2152],{},[397,24543,990],{},[96,24545,24546,24548],{},[84,24547,24533],{},[102,24549,814],{},[550,24551,24552,24554],{},[84,24553,981],{},[76,24555,24556,24558],{},[397,24557,817],{},[84,24559,2152],{},[397,24561,990],{},[397,24563,400],{"stretchy":399},[96,24565,24566,24568],{},[84,24567,20410],{},[102,24569,820],{},[96,24571,24572,24574],{},[84,24573,359],{},[102,24575,820],{},[397,24577,990],{},[96,24579,24580,24582],{},[84,24581,20410],{},[102,24583,814],{},[96,24585,24586,24588],{},[84,24587,359],{},[102,24589,814],{},[397,24591,405],{"stretchy":399},[106,24593,24594],{"encoding":108},"x = C_1 e^t + C_2 e^{-t} + (c_1 x_1 + c_2 x_2)",[60,24596,24598,24616,24703,24793,24891],{"className":24597,"ariaHidden":114},[113],[60,24599,24601,24604,24607,24610,24613],{"className":24600},[118],[60,24602],{"className":24603,"style":371},[122],[60,24605,359],{"className":24606},[127,178],[60,24608],{"className":24609,"style":470},[469],[60,24611,448],{"className":24612},[474],[60,24614],{"className":24615,"style":470},[469],[60,24617,24619,24623,24665,24694,24697,24700],{"className":24618},[118],[60,24620],{"className":24621,"style":24622},[122],"height:0.9436em;vertical-align:-0.15em;",[60,24624,24626,24630],{"className":24625},[127],[60,24627,24533],{"className":24628,"style":24629},[127,178],"margin-right:0.0715em;",[60,24631,24633],{"className":24632},[183],[60,24634,24636,24657],{"className":24635},[139,140],[60,24637,24639,24654],{"className":24638},[144],[60,24640,24642],{"className":24641,"style":318},[148],[60,24643,24645,24648],{"style":24644},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[60,24646],{"className":24647,"style":325},[156],[60,24649,24651],{"className":24650},[161,162,163,164],[60,24652,820],{"className":24653},[127,164],[60,24655,213],{"className":24656},[212],[60,24658,24660],{"className":24659},[144],[60,24661,24663],{"className":24662,"style":341},[148],[60,24664],{},[60,24666,24668,24671],{"className":24667},[127],[60,24669,981],{"className":24670},[127,178],[60,24672,24674],{"className":24673},[183],[60,24675,24677],{"className":24676},[139],[60,24678,24680],{"className":24679},[144],[60,24681,24683],{"className":24682,"style":20132},[148],[60,24684,24685,24688],{"style":608},[60,24686],{"className":24687,"style":325},[156],[60,24689,24691],{"className":24690},[161,162,163,164],[60,24692,2152],{"className":24693},[127,178,164],[60,24695],{"className":24696,"style":924},[469],[60,24698,990],{"className":24699},[928],[60,24701],{"className":24702,"style":924},[469],[60,24704,24706,24709,24749,24784,24787,24790],{"className":24705},[118],[60,24707],{"className":24708,"style":24622},[122],[60,24710,24712,24715],{"className":24711},[127],[60,24713,24533],{"className":24714,"style":24629},[127,178],[60,24716,24718],{"className":24717},[183],[60,24719,24721,24741],{"className":24720},[139,140],[60,24722,24724,24738],{"className":24723},[144],[60,24725,24727],{"className":24726,"style":318},[148],[60,24728,24729,24732],{"style":24644},[60,24730],{"className":24731,"style":325},[156],[60,24733,24735],{"className":24734},[161,162,163,164],[60,24736,814],{"className":24737},[127,164],[60,24739,213],{"className":24740},[212],[60,24742,24744],{"className":24743},[144],[60,24745,24747],{"className":24746,"style":341},[148],[60,24748],{},[60,24750,24752,24755],{"className":24751},[127],[60,24753,981],{"className":24754},[127,178],[60,24756,24758],{"className":24757},[183],[60,24759,24761],{"className":24760},[139],[60,24762,24764],{"className":24763},[144],[60,24765,24767],{"className":24766,"style":20132},[148],[60,24768,24769,24772],{"style":608},[60,24770],{"className":24771,"style":325},[156],[60,24773,24775],{"className":24774},[161,162,163,164],[60,24776,24778,24781],{"className":24777},[127,164],[60,24779,817],{"className":24780},[127,164],[60,24782,2152],{"className":24783},[127,178,164],[60,24785],{"className":24786,"style":924},[469],[60,24788,990],{"className":24789},[928],[60,24791],{"className":24792,"style":924},[469],[60,24794,24796,24799,24802,24842,24882,24885,24888],{"className":24795},[118],[60,24797],{"className":24798,"style":418},[122],[60,24800,400],{"className":24801},[131],[60,24803,24805,24808],{"className":24804},[127],[60,24806,20410],{"className":24807},[127,178],[60,24809,24811],{"className":24810},[183],[60,24812,24814,24834],{"className":24813},[139,140],[60,24815,24817,24831],{"className":24816},[144],[60,24818,24820],{"className":24819,"style":318},[148],[60,24821,24822,24825],{"style":1940},[60,24823],{"className":24824,"style":325},[156],[60,24826,24828],{"className":24827},[161,162,163,164],[60,24829,820],{"className":24830},[127,164],[60,24832,213],{"className":24833},[212],[60,24835,24837],{"className":24836},[144],[60,24838,24840],{"className":24839,"style":341},[148],[60,24841],{},[60,24843,24845,24848],{"className":24844},[127],[60,24846,359],{"className":24847},[127,178],[60,24849,24851],{"className":24850},[183],[60,24852,24854,24874],{"className":24853},[139,140],[60,24855,24857,24871],{"className":24856},[144],[60,24858,24860],{"className":24859,"style":318},[148],[60,24861,24862,24865],{"style":1940},[60,24863],{"className":24864,"style":325},[156],[60,24866,24868],{"className":24867},[161,162,163,164],[60,24869,820],{"className":24870},[127,164],[60,24872,213],{"className":24873},[212],[60,24875,24877],{"className":24876},[144],[60,24878,24880],{"className":24879,"style":341},[148],[60,24881],{},[60,24883],{"className":24884,"style":924},[469],[60,24886,990],{"className":24887},[928],[60,24889],{"className":24890,"style":924},[469],[60,24892,24894,24897,24937,24977],{"className":24893},[118],[60,24895],{"className":24896,"style":418},[122],[60,24898,24900,24903],{"className":24899},[127],[60,24901,20410],{"className":24902},[127,178],[60,24904,24906],{"className":24905},[183],[60,24907,24909,24929],{"className":24908},[139,140],[60,24910,24912,24926],{"className":24911},[144],[60,24913,24915],{"className":24914,"style":318},[148],[60,24916,24917,24920],{"style":1940},[60,24918],{"className":24919,"style":325},[156],[60,24921,24923],{"className":24922},[161,162,163,164],[60,24924,814],{"className":24925},[127,164],[60,24927,213],{"className":24928},[212],[60,24930,24932],{"className":24931},[144],[60,24933,24935],{"className":24934,"style":341},[148],[60,24936],{},[60,24938,24940,24943],{"className":24939},[127],[60,24941,359],{"className":24942},[127,178],[60,24944,24946],{"className":24945},[183],[60,24947,24949,24969],{"className":24948},[139,140],[60,24950,24952,24966],{"className":24951},[144],[60,24953,24955],{"className":24954,"style":318},[148],[60,24956,24957,24960],{"style":1940},[60,24958],{"className":24959,"style":325},[156],[60,24961,24963],{"className":24962},[161,162,163,164],[60,24964,814],{"className":24965},[127,164],[60,24967,213],{"className":24968},[212],[60,24970,24972],{"className":24971},[144],[60,24973,24975],{"className":24974,"style":341},[148],[60,24976],{},[60,24978,405],{"className":24979},[267],"。\n特解部分：\n",[60,24982,24984,25034],{"className":24983},[63],[60,24985,24987],{"className":24986},[67],[69,24988,24989],{"xmlns":71},[73,24990,24991,25031],{},[76,24992,24993,24999,25005,25007,25013,25015,25017,25019,25021,25023,25025,25027,25029],{},[96,24994,24995,24997],{},[84,24996,20410],{},[102,24998,820],{},[550,25000,25001,25003],{},[84,25002,981],{},[84,25004,2152],{},[397,25006,448],{},[79,25008,25009,25011],{},[102,25010,820],{},[102,25012,23145],{},[397,25014,400],{"stretchy":399},[84,25016,9061],{},[397,25018,1465],{},[84,25020,2152],{},[397,25022,817],{},[84,25024,11088],{},[397,25026,1465],{},[84,25028,2152],{},[397,25030,405],{"stretchy":399},[106,25032,25033],{"encoding":108},"c_1 e^t = \\frac{1}{4}(\\sin t - \\cos t)",[60,25035,25037,25121,25216],{"className":25036,"ariaHidden":114},[113],[60,25038,25040,25043,25083,25112,25115,25118],{"className":25039},[118],[60,25041],{"className":25042,"style":24622},[122],[60,25044,25046,25049],{"className":25045},[127],[60,25047,20410],{"className":25048},[127,178],[60,25050,25052],{"className":25051},[183],[60,25053,25055,25075],{"className":25054},[139,140],[60,25056,25058,25072],{"className":25057},[144],[60,25059,25061],{"className":25060,"style":318},[148],[60,25062,25063,25066],{"style":1940},[60,25064],{"className":25065,"style":325},[156],[60,25067,25069],{"className":25068},[161,162,163,164],[60,25070,820],{"className":25071},[127,164],[60,25073,213],{"className":25074},[212],[60,25076,25078],{"className":25077},[144],[60,25079,25081],{"className":25080,"style":341},[148],[60,25082],{},[60,25084,25086,25089],{"className":25085},[127],[60,25087,981],{"className":25088},[127,178],[60,25090,25092],{"className":25091},[183],[60,25093,25095],{"className":25094},[139],[60,25096,25098],{"className":25097},[144],[60,25099,25101],{"className":25100,"style":20132},[148],[60,25102,25103,25106],{"style":608},[60,25104],{"className":25105,"style":325},[156],[60,25107,25109],{"className":25108},[161,162,163,164],[60,25110,2152],{"className":25111},[127,178,164],[60,25113],{"className":25114,"style":470},[469],[60,25116,448],{"className":25117},[474],[60,25119],{"className":25120,"style":470},[469],[60,25122,25124,25127,25195,25198,25201,25204,25207,25210,25213],{"className":25123},[118],[60,25125],{"className":25126,"style":12028},[122],[60,25128,25130,25133,25192],{"className":25129},[127],[60,25131],{"className":25132},[131,132],[60,25134,25136],{"className":25135},[79],[60,25137,25139,25184],{"className":25138},[139,140],[60,25140,25142,25181],{"className":25141},[144],[60,25143,25145,25159,25167],{"className":25144,"style":11547},[148],[60,25146,25147,25150],{"style":152},[60,25148],{"className":25149,"style":157},[156],[60,25151,25153],{"className":25152},[161,162,163,164],[60,25154,25156],{"className":25155},[127,164],[60,25157,23145],{"className":25158},[127,164],[60,25160,25161,25164],{"style":225},[60,25162],{"className":25163,"style":157},[156],[60,25165],{"className":25166,"style":233},[232],[60,25168,25169,25172],{"style":1105},[60,25170],{"className":25171,"style":157},[156],[60,25173,25175],{"className":25174},[161,162,163,164],[60,25176,25178],{"className":25177},[127,164],[60,25179,820],{"className":25180},[127,164],[60,25182,213],{"className":25183},[212],[60,25185,25187],{"className":25186},[144],[60,25188,25190],{"className":25189,"style":3907},[148],[60,25191],{},[60,25193],{"className":25194},[267,132],[60,25196,400],{"className":25197},[131],[60,25199,9061],{"className":25200},[1495],[60,25202],{"className":25203,"style":653},[469],[60,25205,2152],{"className":25206},[127,178],[60,25208],{"className":25209,"style":924},[469],[60,25211,817],{"className":25212},[928],[60,25214],{"className":25215,"style":924},[469],[60,25217,25219,25222,25225,25228,25231],{"className":25218},[118],[60,25220],{"className":25221,"style":418},[122],[60,25223,11088],{"className":25224},[1495],[60,25226],{"className":25227,"style":653},[469],[60,25229,2152],{"className":25230},[127,178],[60,25232,405],{"className":25233},[267],[60,25235,25237,25293],{"className":25236},[63],[60,25238,25240],{"className":25239},[67],[69,25241,25242],{"xmlns":71},[73,25243,25244,25290],{},[76,25245,25246,25252,25262,25264,25266,25272,25274,25276,25278,25280,25282,25284,25286,25288],{},[96,25247,25248,25250],{},[84,25249,20410],{},[102,25251,814],{},[550,25253,25254,25256],{},[84,25255,981],{},[76,25257,25258,25260],{},[397,25259,817],{},[84,25261,2152],{},[397,25263,448],{},[397,25265,817],{},[79,25267,25268,25270],{},[102,25269,820],{},[102,25271,23145],{},[397,25273,400],{"stretchy":399},[84,25275,9061],{},[397,25277,1465],{},[84,25279,2152],{},[397,25281,990],{},[84,25283,11088],{},[397,25285,1465],{},[84,25287,2152],{},[397,25289,405],{"stretchy":399},[106,25291,25292],{"encoding":108},"c_2 e^{-t} = -\\frac{1}{4}(\\sin t + \\cos t)",[60,25294,25296,25386,25484],{"className":25295,"ariaHidden":114},[113],[60,25297,25299,25302,25342,25377,25380,25383],{"className":25298},[118],[60,25300],{"className":25301,"style":24622},[122],[60,25303,25305,25308],{"className":25304},[127],[60,25306,20410],{"className":25307},[127,178],[60,25309,25311],{"className":25310},[183],[60,25312,25314,25334],{"className":25313},[139,140],[60,25315,25317,25331],{"className":25316},[144],[60,25318,25320],{"className":25319,"style":318},[148],[60,25321,25322,25325],{"style":1940},[60,25323],{"className":25324,"style":325},[156],[60,25326,25328],{"className":25327},[161,162,163,164],[60,25329,814],{"className":25330},[127,164],[60,25332,213],{"className":25333},[212],[60,25335,25337],{"className":25336},[144],[60,25338,25340],{"className":25339,"style":341},[148],[60,25341],{},[60,25343,25345,25348],{"className":25344},[127],[60,25346,981],{"className":25347},[127,178],[60,25349,25351],{"className":25350},[183],[60,25352,25354],{"className":25353},[139],[60,25355,25357],{"className":25356},[144],[60,25358,25360],{"className":25359,"style":20132},[148],[60,25361,25362,25365],{"style":608},[60,25363],{"className":25364,"style":325},[156],[60,25366,25368],{"className":25367},[161,162,163,164],[60,25369,25371,25374],{"className":25370},[127,164],[60,25372,817],{"className":25373},[127,164],[60,25375,2152],{"className":25376},[127,178,164],[60,25378],{"className":25379,"style":470},[469],[60,25381,448],{"className":25382},[474],[60,25384],{"className":25385,"style":470},[469],[60,25387,25389,25392,25395,25463,25466,25469,25472,25475,25478,25481],{"className":25388},[118],[60,25390],{"className":25391,"style":12028},[122],[60,25393,817],{"className":25394},[127],[60,25396,25398,25401,25460],{"className":25397},[127],[60,25399],{"className":25400},[131,132],[60,25402,25404],{"className":25403},[79],[60,25405,25407,25452],{"className":25406},[139,140],[60,25408,25410,25449],{"className":25409},[144],[60,25411,25413,25427,25435],{"className":25412,"style":11547},[148],[60,25414,25415,25418],{"style":152},[60,25416],{"className":25417,"style":157},[156],[60,25419,25421],{"className":25420},[161,162,163,164],[60,25422,25424],{"className":25423},[127,164],[60,25425,23145],{"className":25426},[127,164],[60,25428,25429,25432],{"style":225},[60,25430],{"className":25431,"style":157},[156],[60,25433],{"className":25434,"style":233},[232],[60,25436,25437,25440],{"style":1105},[60,25438],{"className":25439,"style":157},[156],[60,25441,25443],{"className":25442},[161,162,163,164],[60,25444,25446],{"className":25445},[127,164],[60,25447,820],{"className":25448},[127,164],[60,25450,213],{"className":25451},[212],[60,25453,25455],{"className":25454},[144],[60,25456,25458],{"className":25457,"style":3907},[148],[60,25459],{},[60,25461],{"className":25462},[267,132],[60,25464,400],{"className":25465},[131],[60,25467,9061],{"className":25468},[1495],[60,25470],{"className":25471,"style":653},[469],[60,25473,2152],{"className":25474},[127,178],[60,25476],{"className":25477,"style":924},[469],[60,25479,990],{"className":25480},[928],[60,25482],{"className":25483,"style":924},[469],[60,25485,25487,25490,25493,25496,25499],{"className":25486},[118],[60,25488],{"className":25489,"style":418},[122],[60,25491,11088],{"className":25492},[1495],[60,25494],{"className":25495,"style":653},[469],[60,25497,2152],{"className":25498},[127,178],[60,25500,405],{"className":25501},[267],"\n特解 ",[60,25504,25506,25598],{"className":25505},[63],[60,25507,25509],{"className":25508},[67],[69,25510,25511],{"xmlns":71},[73,25512,25513,25595],{},[76,25514,25515,25523,25525,25531,25533,25535,25537,25539,25545,25547,25549,25551,25553,25559,25561,25563,25565,25567,25573,25575,25577,25579,25581,25583,25589,25591,25593],{},[25516,25517,25518,25520],"mover",{"accent":114},[84,25519,359],{},[397,25521,25522],{},"ˉ",[397,25524,448],{},[79,25526,25527,25529],{},[102,25528,820],{},[102,25530,23145],{},[84,25532,9061],{},[397,25534,1465],{},[84,25536,2152],{},[397,25538,817],{},[79,25540,25541,25543],{},[102,25542,820],{},[102,25544,23145],{},[84,25546,11088],{},[397,25548,1465],{},[84,25550,2152],{},[397,25552,817],{},[79,25554,25555,25557],{},[102,25556,820],{},[102,25558,23145],{},[84,25560,9061],{},[397,25562,1465],{},[84,25564,2152],{},[397,25566,817],{},[79,25568,25569,25571],{},[102,25570,820],{},[102,25572,23145],{},[84,25574,11088],{},[397,25576,1465],{},[84,25578,2152],{},[397,25580,448],{},[397,25582,817],{},[79,25584,25585,25587],{},[102,25586,820],{},[102,25588,814],{},[84,25590,11088],{},[397,25592,1465],{},[84,25594,2152],{},[106,25596,25597],{"encoding":108},"\\bar{x} = \\frac{1}{4}\\sin t - \\frac{1}{4}\\cos t - \\frac{1}{4}\\sin t - \\frac{1}{4}\\cos t = -\\frac{1}{2}\\cos t",[60,25599,25601,25651,25746,25841,25936,26031],{"className":25600,"ariaHidden":114},[113],[60,25602,25604,25608,25642,25645,25648],{"className":25603},[118],[60,25605],{"className":25606,"style":25607},[122],"height:0.5678em;",[60,25609,25612],{"className":25610},[127,25611],"katex-accent",[60,25613,25615],{"className":25614},[139],[60,25616,25618],{"className":25617},[144],[60,25619,25621,25629],{"className":25620,"style":25607},[148],[60,25622,25623,25626],{"style":19374},[60,25624],{"className":25625,"style":157},[156],[60,25627,359],{"className":25628},[127,178],[60,25630,25631,25634],{"style":19374},[60,25632],{"className":25633,"style":157},[156],[60,25635,25639],{"className":25636,"style":25638},[25637],"accent-body","left:-0.2222em;",[60,25640,25522],{"className":25641},[127],[60,25643],{"className":25644,"style":470},[469],[60,25646,448],{"className":25647},[474],[60,25649],{"className":25650,"style":470},[469],[60,25652,25654,25657,25725,25728,25731,25734,25737,25740,25743],{"className":25653},[118],[60,25655],{"className":25656,"style":12028},[122],[60,25658,25660,25663,25722],{"className":25659},[127],[60,25661],{"className":25662},[131,132],[60,25664,25666],{"className":25665},[79],[60,25667,25669,25714],{"className":25668},[139,140],[60,25670,25672,25711],{"className":25671},[144],[60,25673,25675,25689,25697],{"className":25674,"style":11547},[148],[60,25676,25677,25680],{"style":152},[60,25678],{"className":25679,"style":157},[156],[60,25681,25683],{"className":25682},[161,162,163,164],[60,25684,25686],{"className":25685},[127,164],[60,25687,23145],{"className":25688},[127,164],[60,25690,25691,25694],{"style":225},[60,25692],{"className":25693,"style":157},[156],[60,25695],{"className":25696,"style":233},[232],[60,25698,25699,25702],{"style":1105},[60,25700],{"className":25701,"style":157},[156],[60,25703,25705],{"className":25704},[161,162,163,164],[60,25706,25708],{"className":25707},[127,164],[60,25709,820],{"className":25710},[127,164],[60,25712,213],{"className":25713},[212],[60,25715,25717],{"className":25716},[144],[60,25718,25720],{"className":25719,"style":3907},[148],[60,25721],{},[60,25723],{"className":25724},[267,132],[60,25726],{"className":25727,"style":653},[469],[60,25729,9061],{"className":25730},[1495],[60,25732],{"className":25733,"style":653},[469],[60,25735,2152],{"className":25736},[127,178],[60,25738],{"className":25739,"style":924},[469],[60,25741,817],{"className":25742},[928],[60,25744],{"className":25745,"style":924},[469],[60,25747,25749,25752,25820,25823,25826,25829,25832,25835,25838],{"className":25748},[118],[60,25750],{"className":25751,"style":12028},[122],[60,25753,25755,25758,25817],{"className":25754},[127],[60,25756],{"className":25757},[131,132],[60,25759,25761],{"className":25760},[79],[60,25762,25764,25809],{"className":25763},[139,140],[60,25765,25767,25806],{"className":25766},[144],[60,25768,25770,25784,25792],{"className":25769,"style":11547},[148],[60,25771,25772,25775],{"style":152},[60,25773],{"className":25774,"style":157},[156],[60,25776,25778],{"className":25777},[161,162,163,164],[60,25779,25781],{"className":25780},[127,164],[60,25782,23145],{"className":25783},[127,164],[60,25785,25786,25789],{"style":225},[60,25787],{"className":25788,"style":157},[156],[60,25790],{"className":25791,"style":233},[232],[60,25793,25794,25797],{"style":1105},[60,25795],{"className":25796,"style":157},[156],[60,25798,25800],{"className":25799},[161,162,163,164],[60,25801,25803],{"className":25802},[127,164],[60,25804,820],{"className":25805},[127,164],[60,25807,213],{"className":25808},[212],[60,25810,25812],{"className":25811},[144],[60,25813,25815],{"className":25814,"style":3907},[148],[60,25816],{},[60,25818],{"className":25819},[267,132],[60,25821],{"className":25822,"style":653},[469],[60,25824,11088],{"className":25825},[1495],[60,25827],{"className":25828,"style":653},[469],[60,25830,2152],{"className":25831},[127,178],[60,25833],{"className":25834,"style":924},[469],[60,25836,817],{"className":25837},[928],[60,25839],{"className":25840,"style":924},[469],[60,25842,25844,25847,25915,25918,25921,25924,25927,25930,25933],{"className":25843},[118],[60,25845],{"className":25846,"style":12028},[122],[60,25848,25850,25853,25912],{"className":25849},[127],[60,25851],{"className":25852},[131,132],[60,25854,25856],{"className":25855},[79],[60,25857,25859,25904],{"className":25858},[139,140],[60,25860,25862,25901],{"className":25861},[144],[60,25863,25865,25879,25887],{"className":25864,"style":11547},[148],[60,25866,25867,25870],{"style":152},[60,25868],{"className":25869,"style":157},[156],[60,25871,25873],{"className":25872},[161,162,163,164],[60,25874,25876],{"className":25875},[127,164],[60,25877,23145],{"className":25878},[127,164],[60,25880,25881,25884],{"style":225},[60,25882],{"className":25883,"style":157},[156],[60,25885],{"className":25886,"style":233},[232],[60,25888,25889,25892],{"style":1105},[60,25890],{"className":25891,"style":157},[156],[60,25893,25895],{"className":25894},[161,162,163,164],[60,25896,25898],{"className":25897},[127,164],[60,25899,820],{"className":25900},[127,164],[60,25902,213],{"className":25903},[212],[60,25905,25907],{"className":25906},[144],[60,25908,25910],{"className":25909,"style":3907},[148],[60,25911],{},[60,25913],{"className":25914},[267,132],[60,25916],{"className":25917,"style":653},[469],[60,25919,9061],{"className":25920},[1495],[60,25922],{"className":25923,"style":653},[469],[60,25925,2152],{"className":25926},[127,178],[60,25928],{"className":25929,"style":924},[469],[60,25931,817],{"className":25932},[928],[60,25934],{"className":25935,"style":924},[469],[60,25937,25939,25942,26010,26013,26016,26019,26022,26025,26028],{"className":25938},[118],[60,25940],{"className":25941,"style":12028},[122],[60,25943,25945,25948,26007],{"className":25944},[127],[60,25946],{"className":25947},[131,132],[60,25949,25951],{"className":25950},[79],[60,25952,25954,25999],{"className":25953},[139,140],[60,25955,25957,25996],{"className":25956},[144],[60,25958,25960,25974,25982],{"className":25959,"style":11547},[148],[60,25961,25962,25965],{"style":152},[60,25963],{"className":25964,"style":157},[156],[60,25966,25968],{"className":25967},[161,162,163,164],[60,25969,25971],{"className":25970},[127,164],[60,25972,23145],{"className":25973},[127,164],[60,25975,25976,25979],{"style":225},[60,25977],{"className":25978,"style":157},[156],[60,25980],{"className":25981,"style":233},[232],[60,25983,25984,25987],{"style":1105},[60,25985],{"className":25986,"style":157},[156],[60,25988,25990],{"className":25989},[161,162,163,164],[60,25991,25993],{"className":25992},[127,164],[60,25994,820],{"className":25995},[127,164],[60,25997,213],{"className":25998},[212],[60,26000,26002],{"className":26001},[144],[60,26003,26005],{"className":26004,"style":3907},[148],[60,26006],{},[60,26008],{"className":26009},[267,132],[60,26011],{"className":26012,"style":653},[469],[60,26014,11088],{"className":26015},[1495],[60,26017],{"className":26018,"style":653},[469],[60,26020,2152],{"className":26021},[127,178],[60,26023],{"className":26024,"style":470},[469],[60,26026,448],{"className":26027},[474],[60,26029],{"className":26030,"style":470},[469],[60,26032,26034,26037,26040,26108,26111,26114,26117],{"className":26033},[118],[60,26035],{"className":26036,"style":12028},[122],[60,26038,817],{"className":26039},[127],[60,26041,26043,26046,26105],{"className":26042},[127],[60,26044],{"className":26045},[131,132],[60,26047,26049],{"className":26048},[79],[60,26050,26052,26097],{"className":26051},[139,140],[60,26053,26055,26094],{"className":26054},[144],[60,26056,26058,26072,26080],{"className":26057,"style":11547},[148],[60,26059,26060,26063],{"style":152},[60,26061],{"className":26062,"style":157},[156],[60,26064,26066],{"className":26065},[161,162,163,164],[60,26067,26069],{"className":26068},[127,164],[60,26070,814],{"className":26071},[127,164],[60,26073,26074,26077],{"style":225},[60,26075],{"className":26076,"style":157},[156],[60,26078],{"className":26079,"style":233},[232],[60,26081,26082,26085],{"style":1105},[60,26083],{"className":26084,"style":157},[156],[60,26086,26088],{"className":26087},[161,162,163,164],[60,26089,26091],{"className":26090},[127,164],[60,26092,820],{"className":26093},[127,164],[60,26095,213],{"className":26096},[212],[60,26098,26100],{"className":26099},[144],[60,26101,26103],{"className":26102,"style":3907},[148],[60,26104],{},[60,26106],{"className":26107},[267,132],[60,26109],{"className":26110,"style":653},[469],[60,26112,11088],{"className":26113},[1495],[60,26115],{"className":26116,"style":653},[469],[60,26118,2152],{"className":26119},[127,178],[23,26121,26122,13724,26125],{},[26,26123,26124],{},"最终结果：",[60,26126,26128,26188],{"className":26127},[63],[60,26129,26131],{"className":26130},[67],[69,26132,26133],{"xmlns":71},[73,26134,26135,26185],{},[76,26136,26137,26139,26141,26147,26153,26155,26161,26171,26173,26179,26181,26183],{},[84,26138,359],{},[397,26140,448],{},[96,26142,26143,26145],{},[84,26144,24533],{},[102,26146,820],{},[550,26148,26149,26151],{},[84,26150,981],{},[84,26152,2152],{},[397,26154,990],{},[96,26156,26157,26159],{},[84,26158,24533],{},[102,26160,814],{},[550,26162,26163,26165],{},[84,26164,981],{},[76,26166,26167,26169],{},[397,26168,817],{},[84,26170,2152],{},[397,26172,817],{},[79,26174,26175,26177],{},[102,26176,820],{},[102,26178,814],{},[84,26180,11088],{},[397,26182,1465],{},[84,26184,2152],{},[106,26186,26187],{"encoding":108},"x = C_1 e^t + C_2 e^{-t} - \\frac{1}{2}\\cos t",[60,26189,26191,26209,26293,26383],{"className":26190,"ariaHidden":114},[113],[60,26192,26194,26197,26200,26203,26206],{"className":26193},[118],[60,26195],{"className":26196,"style":371},[122],[60,26198,359],{"className":26199},[127,178],[60,26201],{"className":26202,"style":470},[469],[60,26204,448],{"className":26205},[474],[60,26207],{"className":26208,"style":470},[469],[60,26210,26212,26215,26255,26284,26287,26290],{"className":26211},[118],[60,26213],{"className":26214,"style":24622},[122],[60,26216,26218,26221],{"className":26217},[127],[60,26219,24533],{"className":26220,"style":24629},[127,178],[60,26222,26224],{"className":26223},[183],[60,26225,26227,26247],{"className":26226},[139,140],[60,26228,26230,26244],{"className":26229},[144],[60,26231,26233],{"className":26232,"style":318},[148],[60,26234,26235,26238],{"style":24644},[60,26236],{"className":26237,"style":325},[156],[60,26239,26241],{"className":26240},[161,162,163,164],[60,26242,820],{"className":26243},[127,164],[60,26245,213],{"className":26246},[212],[60,26248,26250],{"className":26249},[144],[60,26251,26253],{"className":26252,"style":341},[148],[60,26254],{},[60,26256,26258,26261],{"className":26257},[127],[60,26259,981],{"className":26260},[127,178],[60,26262,26264],{"className":26263},[183],[60,26265,26267],{"className":26266},[139],[60,26268,26270],{"className":26269},[144],[60,26271,26273],{"className":26272,"style":20132},[148],[60,26274,26275,26278],{"style":608},[60,26276],{"className":26277,"style":325},[156],[60,26279,26281],{"className":26280},[161,162,163,164],[60,26282,2152],{"className":26283},[127,178,164],[60,26285],{"className":26286,"style":924},[469],[60,26288,990],{"className":26289},[928],[60,26291],{"className":26292,"style":924},[469],[60,26294,26296,26299,26339,26374,26377,26380],{"className":26295},[118],[60,26297],{"className":26298,"style":24622},[122],[60,26300,26302,26305],{"className":26301},[127],[60,26303,24533],{"className":26304,"style":24629},[127,178],[60,26306,26308],{"className":26307},[183],[60,26309,26311,26331],{"className":26310},[139,140],[60,26312,26314,26328],{"className":26313},[144],[60,26315,26317],{"className":26316,"style":318},[148],[60,26318,26319,26322],{"style":24644},[60,26320],{"className":26321,"style":325},[156],[60,26323,26325],{"className":26324},[161,162,163,164],[60,26326,814],{"className":26327},[127,164],[60,26329,213],{"className":26330},[212],[60,26332,26334],{"className":26333},[144],[60,26335,26337],{"className":26336,"style":341},[148],[60,26338],{},[60,26340,26342,26345],{"className":26341},[127],[60,26343,981],{"className":26344},[127,178],[60,26346,26348],{"className":26347},[183],[60,26349,26351],{"className":26350},[139],[60,26352,26354],{"className":26353},[144],[60,26355,26357],{"className":26356,"style":20132},[148],[60,26358,26359,26362],{"style":608},[60,26360],{"className":26361,"style":325},[156],[60,26363,26365],{"className":26364},[161,162,163,164],[60,26366,26368,26371],{"className":26367},[127,164],[60,26369,817],{"className":26370},[127,164],[60,26372,2152],{"className":26373},[127,178,164],[60,26375],{"className":26376,"style":924},[469],[60,26378,817],{"className":26379},[928],[60,26381],{"className":26382,"style":924},[469],[60,26384,26386,26389,26457,26460,26463,26466],{"className":26385},[118],[60,26387],{"className":26388,"style":12028},[122],[60,26390,26392,26395,26454],{"className":26391},[127],[60,26393],{"className":26394},[131,132],[60,26396,26398],{"className":26397},[79],[60,26399,26401,26446],{"className":26400},[139,140],[60,26402,26404,26443],{"className":26403},[144],[60,26405,26407,26421,26429],{"className":26406,"style":11547},[148],[60,26408,26409,26412],{"style":152},[60,26410],{"className":26411,"style":157},[156],[60,26413,26415],{"className":26414},[161,162,163,164],[60,26416,26418],{"className":26417},[127,164],[60,26419,814],{"className":26420},[127,164],[60,26422,26423,26426],{"style":225},[60,26424],{"className":26425,"style":157},[156],[60,26427],{"className":26428,"style":233},[232],[60,26430,26431,26434],{"style":1105},[60,26432],{"className":26433,"style":157},[156],[60,26435,26437],{"className":26436},[161,162,163,164],[60,26438,26440],{"className":26439},[127,164],[60,26441,820],{"className":26442},[127,164],[60,26444,213],{"className":26445},[212],[60,26447,26449],{"className":26448},[144],[60,26450,26452],{"className":26451,"style":3907},[148],[60,26453],{},[60,26455],{"className":26456},[267,132],[60,26458],{"className":26459,"style":653},[469],[60,26461,11088],{"className":26462},[1495],[60,26464],{"className":26465,"style":653},[469],[60,26467,2152],{"className":26468},[127,178],[15,26470],{},[496,26472,26474,26475,19999,26614],{"id":26473},"_3-x4xtsin2tx-4x-tsin-2tx4xtsin2t已知-x1cos2tx2sin2tx_1-cos-2t-x_2-sin-2tx1cos2tx2sin2t","(3) ",[60,26476,26478,26518],{"className":26477},[63],[60,26479,26481],{"className":26480},[67],[69,26482,26483],{"xmlns":71},[73,26484,26485,26515],{},[76,26486,26487,26497,26499,26501,26503,26505,26507,26509,26511,26513],{},[550,26488,26489,26491],{},[84,26490,359],{},[76,26492,26493,26495],{},[397,26494,557],{"mathvariant":86},[397,26496,557],{"mathvariant":86},[397,26498,990],{},[102,26500,23145],{},[84,26502,359],{},[397,26504,448],{},[84,26506,2152],{},[84,26508,9061],{},[397,26510,1465],{},[102,26512,814],{},[84,26514,2152],{},[106,26516,26517],{"encoding":108},"x'' + 4x = t\\sin 2t",[60,26519,26521,26568,26589],{"className":26520,"ariaHidden":114},[113],[60,26522,26524,26527,26559,26562,26565],{"className":26523},[118],[60,26525],{"className":26526,"style":19924},[122],[60,26528,26530,26533],{"className":26529},[127],[60,26531,359],{"className":26532},[127,178],[60,26534,26536],{"className":26535},[183],[60,26537,26539],{"className":26538},[139],[60,26540,26542],{"className":26541},[144],[60,26543,26545],{"className":26544,"style":605},[148],[60,26546,26547,26550],{"style":608},[60,26548],{"className":26549,"style":325},[156],[60,26551,26553],{"className":26552},[161,162,163,164],[60,26554,26556],{"className":26555},[127,164],[60,26557,17727],{"className":26558},[127,164],[60,26560],{"className":26561,"style":924},[469],[60,26563,990],{"className":26564},[928],[60,26566],{"className":26567,"style":924},[469],[60,26569,26571,26574,26577,26580,26583,26586],{"className":26570},[118],[60,26572],{"className":26573,"style":484},[122],[60,26575,23145],{"className":26576},[127],[60,26578,359],{"className":26579},[127,178],[60,26581],{"className":26582,"style":470},[469],[60,26584,448],{"className":26585},[474],[60,26587],{"className":26588,"style":470},[469],[60,26590,26592,26596,26599,26602,26605,26608,26611],{"className":26591},[118],[60,26593],{"className":26594,"style":26595},[122],"height:0.6679em;",[60,26597,2152],{"className":26598},[127,178],[60,26600],{"className":26601,"style":653},[469],[60,26603,9061],{"className":26604},[1495],[60,26606],{"className":26607,"style":653},[469],[60,26609,814],{"className":26610},[127],[60,26612,2152],{"className":26613},[127,178],[60,26615,26617,26663],{"className":26616},[63],[60,26618,26620],{"className":26619},[67],[69,26621,26622],{"xmlns":71},[73,26623,26624,26660],{},[76,26625,26626,26632,26634,26636,26638,26640,26642,26644,26650,26652,26654,26656,26658],{},[96,26627,26628,26630],{},[84,26629,359],{},[102,26631,820],{},[397,26633,448],{},[84,26635,11088],{},[397,26637,1465],{},[102,26639,814],{},[84,26641,2152],{},[397,26643,569],{"separator":114},[96,26645,26646,26648],{},[84,26647,359],{},[102,26649,814],{},[397,26651,448],{},[84,26653,9061],{},[397,26655,1465],{},[102,26657,814],{},[84,26659,2152],{},[106,26661,26662],{"encoding":108},"x_1 = \\cos 2t, x_2 = \\sin 2t",[60,26664,26666,26721,26794],{"className":26665,"ariaHidden":114},[113],[60,26667,26669,26672,26712,26715,26718],{"className":26668},[118],[60,26670],{"className":26671,"style":2734},[122],[60,26673,26675,26678],{"className":26674},[127],[60,26676,359],{"className":26677},[127,178],[60,26679,26681],{"className":26680},[183],[60,26682,26684,26704],{"className":26683},[139,140],[60,26685,26687,26701],{"className":26686},[144],[60,26688,26690],{"className":26689,"style":318},[148],[60,26691,26692,26695],{"style":1940},[60,26693],{"className":26694,"style":325},[156],[60,26696,26698],{"className":26697},[161,162,163,164],[60,26699,820],{"className":26700},[127,164],[60,26702,213],{"className":26703},[212],[60,26705,26707],{"className":26706},[144],[60,26708,26710],{"className":26709,"style":341},[148],[60,26711],{},[60,26713],{"className":26714,"style":470},[469],[60,26716,448],{"className":26717},[474],[60,26719],{"className":26720,"style":470},[469],[60,26722,26724,26727,26730,26733,26736,26739,26742,26745,26785,26788,26791],{"className":26723},[118],[60,26725],{"className":26726,"style":9657},[122],[60,26728,11088],{"className":26729},[1495],[60,26731],{"className":26732,"style":653},[469],[60,26734,814],{"className":26735},[127],[60,26737,2152],{"className":26738},[127,178],[60,26740,569],{"className":26741},[649],[60,26743],{"className":26744,"style":653},[469],[60,26746,26748,26751],{"className":26747},[127],[60,26749,359],{"className":26750},[127,178],[60,26752,26754],{"className":26753},[183],[60,26755,26757,26777],{"className":26756},[139,140],[60,26758,26760,26774],{"className":26759},[144],[60,26761,26763],{"className":26762,"style":318},[148],[60,26764,26765,26768],{"style":1940},[60,26766],{"className":26767,"style":325},[156],[60,26769,26771],{"className":26770},[161,162,163,164],[60,26772,814],{"className":26773},[127,164],[60,26775,213],{"className":26776},[212],[60,26778,26780],{"className":26779},[144],[60,26781,26783],{"className":26782,"style":341},[148],[60,26784],{},[60,26786],{"className":26787,"style":470},[469],[60,26789,448],{"className":26790},[474],[60,26792],{"className":26793,"style":470},[469],[60,26795,26797,26800,26803,26806,26809],{"className":26796},[118],[60,26798],{"className":26799,"style":26595},[122],[60,26801,9061],{"className":26802},[1495],[60,26804],{"className":26805,"style":653},[469],[60,26807,814],{"className":26808},[127],[60,26810,2152],{"className":26811},[127,178],[23,26813,26814,26816,26881,26882,488],{},[26,26815,20244],{},[60,26817,26819,26840],{"className":26818},[63],[60,26820,26822],{"className":26821},[67],[69,26823,26824],{"xmlns":71},[73,26825,26826,26838],{},[76,26827,26828],{},[550,26829,26830,26832],{},[84,26831,359],{},[76,26833,26834,26836],{},[397,26835,557],{"mathvariant":86},[397,26837,557],{"mathvariant":86},[106,26839,20269],{"encoding":108},[60,26841,26843],{"className":26842,"ariaHidden":114},[113],[60,26844,26846,26849],{"className":26845},[118],[60,26847],{"className":26848,"style":605},[122],[60,26850,26852,26855],{"className":26851},[127],[60,26853,359],{"className":26854},[127,178],[60,26856,26858],{"className":26857},[183],[60,26859,26861],{"className":26860},[139],[60,26862,26864],{"className":26863},[144],[60,26865,26867],{"className":26866,"style":605},[148],[60,26868,26869,26872],{"style":608},[60,26870],{"className":26871,"style":325},[156],[60,26873,26875],{"className":26874},[161,162,163,164],[60,26876,26878],{"className":26877},[127,164],[60,26879,17727],{"className":26880},[127,164]," 前系数为 1，合格。",[60,26883,26885,26917],{"className":26884},[63],[60,26886,26888],{"className":26887},[67],[69,26889,26890],{"xmlns":71},[73,26891,26892,26914],{},[76,26893,26894,26896,26898,26900,26902,26904,26906,26908,26910,26912],{},[84,26895,562],{},[397,26897,400],{"stretchy":399},[84,26899,2152],{},[397,26901,405],{"stretchy":399},[397,26903,448],{},[84,26905,2152],{},[84,26907,9061],{},[397,26909,1465],{},[102,26911,814],{},[84,26913,2152],{},[106,26915,26916],{"encoding":108},"f(t) = t\\sin 2t",[60,26918,26920,26947],{"className":26919,"ariaHidden":114},[113],[60,26921,26923,26926,26929,26932,26935,26938,26941,26944],{"className":26922},[118],[60,26924],{"className":26925,"style":418},[122],[60,26927,562],{"className":26928,"style":639},[127,178],[60,26930,400],{"className":26931},[131],[60,26933,2152],{"className":26934},[127,178],[60,26936,405],{"className":26937},[267],[60,26939],{"className":26940,"style":470},[469],[60,26942,448],{"className":26943},[474],[60,26945],{"className":26946,"style":470},[469],[60,26948,26950,26953,26956,26959,26962,26965,26968],{"className":26949},[118],[60,26951],{"className":26952,"style":26595},[122],[60,26954,2152],{"className":26955},[127,178],[60,26957],{"className":26958,"style":653},[469],[60,26960,9061],{"className":26961},[1495],[60,26963],{"className":26964,"style":653},[469],[60,26966,814],{"className":26967},[127],[60,26969,2152],{"className":26970},[127,178],[23,26972,26973,26976,26977,21834],{},[26,26974,26975],{},"Step 2: 列方程组","\n[\n",[60,26978,26980,27110],{"className":26979},[63],[60,26981,26983],{"className":26982},[67],[69,26984,26985],{"xmlns":71},[73,26986,26987,27107],{},[76,26988,26989,26991],{},[397,26990,20568],{"fence":114},[20570,26992,26993,27039],{"rowspacing":20572,"columnalign":20573,"columnspacing":13091},[20575,26994,26995],{},[20578,26996,26997],{},[20581,26998,26999],{"scriptlevel":104,"displaystyle":399},[76,27000,27001,27009,27011,27013,27015,27017,27019,27027,27029,27031,27033,27035,27037],{},[2127,27002,27003,27005,27007],{},[84,27004,20410],{},[102,27006,820],{},[397,27008,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,27010,11088],{},[397,27012,1465],{},[102,27014,814],{},[84,27016,2152],{},[397,27018,990],{},[2127,27020,27021,27023,27025],{},[84,27022,20410],{},[102,27024,814],{},[397,27026,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,27028,9061],{},[397,27030,1465],{},[102,27032,814],{},[84,27034,2152],{},[397,27036,448],{},[102,27038,104],{},[20575,27040,27041],{},[20578,27042,27043],{},[20581,27044,27045],{"scriptlevel":104,"displaystyle":399},[76,27046,27047,27055,27057,27059,27061,27063,27065,27067,27069,27071,27073,27081,27083,27085,27087,27089,27091,27093,27095,27097,27099,27101,27103,27105],{},[2127,27048,27049,27051,27053],{},[84,27050,20410],{},[102,27052,820],{},[397,27054,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,27056,400],{"stretchy":399},[397,27058,817],{},[102,27060,814],{},[84,27062,9061],{},[397,27064,1465],{},[102,27066,814],{},[84,27068,2152],{},[397,27070,405],{"stretchy":399},[397,27072,990],{},[2127,27074,27075,27077,27079],{},[84,27076,20410],{},[102,27078,814],{},[397,27080,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,27082,400],{"stretchy":399},[102,27084,814],{},[84,27086,11088],{},[397,27088,1465],{},[102,27090,814],{},[84,27092,2152],{},[397,27094,405],{"stretchy":399},[397,27096,448],{},[84,27098,2152],{},[84,27100,9061],{},[397,27102,1465],{},[102,27104,814],{},[84,27106,2152],{},[106,27108,27109],{"encoding":108},"\\begin{cases}\nc_1' \\cos 2t + c_2' \\sin 2t = 0 \\\\\nc_1' (-2\\sin 2t) + c_2' (2\\cos 2t) = t\\sin 2t\n\\end{cases}",[60,27111,27113],{"className":27112,"ariaHidden":114},[113],[60,27114,27116,27119],{"className":27115},[118],[60,27117],{"className":27118,"style":20819},[122],[60,27120,27122,27128,27527],{"className":27121},[2326],[60,27123,27125],{"className":27124,"style":2331},[131,2330],[60,27126,20568],{"className":27127},[2335,20829],[60,27129,27131],{"className":27130},[127],[60,27132,27134],{"className":27133},[20570],[60,27135,27137],{"className":27136},[20839],[60,27138,27140,27519],{"className":27139},[139,140],[60,27141,27143,27516],{"className":27142},[144],[60,27144,27146,27313],{"className":27145,"style":20849},[148],[60,27147,27148,27151],{"style":20852},[60,27149],{"className":27150,"style":20856},[156],[60,27152,27154,27208,27211,27214,27217,27220,27223,27226,27229,27232,27286,27289,27292,27295,27298,27301,27304,27307,27310],{"className":27153},[127],[60,27155,27157,27160],{"className":27156},[127],[60,27158,20410],{"className":27159},[127,178],[60,27161,27163],{"className":27162},[183],[60,27164,27166,27200],{"className":27165},[139,140],[60,27167,27169,27197],{"className":27168},[144],[60,27170,27172,27183],{"className":27171,"style":605},[148],[60,27173,27174,27177],{"style":17413},[60,27175],{"className":27176,"style":325},[156],[60,27178,27180],{"className":27179},[161,162,163,164],[60,27181,820],{"className":27182},[127,164],[60,27184,27185,27188],{"style":608},[60,27186],{"className":27187,"style":325},[156],[60,27189,27191],{"className":27190},[161,162,163,164],[60,27192,27194],{"className":27193},[127,164],[60,27195,557],{"className":27196},[127,164],[60,27198,213],{"className":27199},[212],[60,27201,27203],{"className":27202},[144],[60,27204,27206],{"className":27205,"style":17446},[148],[60,27207],{},[60,27209],{"className":27210,"style":653},[469],[60,27212,11088],{"className":27213},[1495],[60,27215],{"className":27216,"style":653},[469],[60,27218,814],{"className":27219},[127],[60,27221,2152],{"className":27222},[127,178],[60,27224],{"className":27225,"style":924},[469],[60,27227,990],{"className":27228},[928],[60,27230],{"className":27231,"style":924},[469],[60,27233,27235,27238],{"className":27234},[127],[60,27236,20410],{"className":27237},[127,178],[60,27239,27241],{"className":27240},[183],[60,27242,27244,27278],{"className":27243},[139,140],[60,27245,27247,27275],{"className":27246},[144],[60,27248,27250,27261],{"className":27249,"style":605},[148],[60,27251,27252,27255],{"style":17413},[60,27253],{"className":27254,"style":325},[156],[60,27256,27258],{"className":27257},[161,162,163,164],[60,27259,814],{"className":27260},[127,164],[60,27262,27263,27266],{"style":608},[60,27264],{"className":27265,"style":325},[156],[60,27267,27269],{"className":27268},[161,162,163,164],[60,27270,27272],{"className":27271},[127,164],[60,27273,557],{"className":27274},[127,164],[60,27276,213],{"className":27277},[212],[60,27279,27281],{"className":27280},[144],[60,27282,27284],{"className":27283,"style":17446},[148],[60,27285],{},[60,27287],{"className":27288,"style":653},[469],[60,27290,9061],{"className":27291},[1495],[60,27293],{"className":27294,"style":653},[469],[60,27296,814],{"className":27297},[127],[60,27299,2152],{"className":27300},[127,178],[60,27302],{"className":27303,"style":470},[469],[60,27305,448],{"className":27306},[474],[60,27308],{"className":27309,"style":470},[469],[60,27311,104],{"className":27312},[127],[60,27314,27315,27318],{"style":21055},[60,27316],{"className":27317,"style":20856},[156],[60,27319,27321,27375,27378,27381,27384,27387,27390,27393,27396,27399,27402,27405,27408,27411,27465,27468,27471,27474,27477,27480,27483,27486,27489,27492,27495,27498,27501,27504,27507,27510,27513],{"className":27320},[127],[60,27322,27324,27327],{"className":27323},[127],[60,27325,20410],{"className":27326},[127,178],[60,27328,27330],{"className":27329},[183],[60,27331,27333,27367],{"className":27332},[139,140],[60,27334,27336,27364],{"className":27335},[144],[60,27337,27339,27350],{"className":27338,"style":605},[148],[60,27340,27341,27344],{"style":17413},[60,27342],{"className":27343,"style":325},[156],[60,27345,27347],{"className":27346},[161,162,163,164],[60,27348,820],{"className":27349},[127,164],[60,27351,27352,27355],{"style":608},[60,27353],{"className":27354,"style":325},[156],[60,27356,27358],{"className":27357},[161,162,163,164],[60,27359,27361],{"className":27360},[127,164],[60,27362,557],{"className":27363},[127,164],[60,27365,213],{"className":27366},[212],[60,27368,27370],{"className":27369},[144],[60,27371,27373],{"className":27372,"style":17446},[148],[60,27374],{},[60,27376,400],{"className":27377},[131],[60,27379,817],{"className":27380},[127],[60,27382,814],{"className":27383},[127],[60,27385],{"className":27386,"style":653},[469],[60,27388,9061],{"className":27389},[1495],[60,27391],{"className":27392,"style":653},[469],[60,27394,814],{"className":27395},[127],[60,27397,2152],{"className":27398},[127,178],[60,27400,405],{"className":27401},[267],[60,27403],{"className":27404,"style":924},[469],[60,27406,990],{"className":27407},[928],[60,27409],{"className":27410,"style":924},[469],[60,27412,27414,27417],{"className":27413},[127],[60,27415,20410],{"className":27416},[127,178],[60,27418,27420],{"className":27419},[183],[60,27421,27423,27457],{"className":27422},[139,140],[60,27424,27426,27454],{"className":27425},[144],[60,27427,27429,27440],{"className":27428,"style":605},[148],[60,27430,27431,27434],{"style":17413},[60,27432],{"className":27433,"style":325},[156],[60,27435,27437],{"className":27436},[161,162,163,164],[60,27438,814],{"className":27439},[127,164],[60,27441,27442,27445],{"style":608},[60,27443],{"className":27444,"style":325},[156],[60,27446,27448],{"className":27447},[161,162,163,164],[60,27449,27451],{"className":27450},[127,164],[60,27452,557],{"className":27453},[127,164],[60,27455,213],{"className":27456},[212],[60,27458,27460],{"className":27459},[144],[60,27461,27463],{"className":27462,"style":17446},[148],[60,27464],{},[60,27466,400],{"className":27467},[131],[60,27469,814],{"className":27470},[127],[60,27472],{"className":27473,"style":653},[469],[60,27475,11088],{"className":27476},[1495],[60,27478],{"className":27479,"style":653},[469],[60,27481,814],{"className":27482},[127],[60,27484,2152],{"className":27485},[127,178],[60,27487,405],{"className":27488},[267],[60,27490],{"className":27491,"style":470},[469],[60,27493,448],{"className":27494},[474],[60,27496],{"className":27497,"style":470},[469],[60,27499,2152],{"className":27500},[127,178],[60,27502],{"className":27503,"style":653},[469],[60,27505,9061],{"className":27506},[1495],[60,27508],{"className":27509,"style":653},[469],[60,27511,814],{"className":27512},[127],[60,27514,2152],{"className":27515},[127,178],[60,27517,213],{"className":27518},[212],[60,27520,27522],{"className":27521},[144],[60,27523,27525],{"className":27524,"style":21340},[148],[60,27526],{},[60,27528],{"className":27529},[267,132],[23,27531,27532,27534],{},[26,27533,21839],{},"\n这是一个二元一次方程组。",[51,27536,27537,28552],{},[33,27538,27539,27540,27592,27593,27637,27638,12545,27724,28045,28323],{},"将第一式乘以 ",[60,27541,27543,27565],{"className":27542},[63],[60,27544,27546],{"className":27545},[67],[69,27547,27548],{"xmlns":71},[73,27549,27550,27562],{},[76,27551,27552,27554,27556,27558,27560],{},[102,27553,814],{},[84,27555,9061],{},[397,27557,1465],{},[102,27559,814],{},[84,27561,2152],{},[106,27563,27564],{"encoding":108},"2\\sin 2t",[60,27566,27568],{"className":27567,"ariaHidden":114},[113],[60,27569,27571,27574,27577,27580,27583,27586,27589],{"className":27570},[118],[60,27572],{"className":27573,"style":26595},[122],[60,27575,814],{"className":27576},[127],[60,27578],{"className":27579,"style":653},[469],[60,27581,9061],{"className":27582},[1495],[60,27584],{"className":27585,"style":653},[469],[60,27587,814],{"className":27588},[127],[60,27590,2152],{"className":27591},[127,178],"，第二式乘以 ",[60,27594,27596,27616],{"className":27595},[63],[60,27597,27599],{"className":27598},[67],[69,27600,27601],{"xmlns":71},[73,27602,27603,27613],{},[76,27604,27605,27607,27609,27611],{},[84,27606,11088],{},[397,27608,1465],{},[102,27610,814],{},[84,27612,2152],{},[106,27614,27615],{"encoding":108},"\\cos 2t",[60,27617,27619],{"className":27618,"ariaHidden":114},[113],[60,27620,27622,27625,27628,27631,27634],{"className":27621},[118],[60,27623],{"className":27624,"style":484},[122],[60,27626,11088],{"className":27627},[1495],[60,27629],{"className":27630,"style":653},[469],[60,27632,814],{"className":27633},[127],[60,27635,2152],{"className":27636},[127,178],"，相加消去 ",[60,27639,27641,27661],{"className":27640},[63],[60,27642,27644],{"className":27643},[67],[69,27645,27646],{"xmlns":71},[73,27647,27648,27658],{},[76,27649,27650],{},[2127,27651,27652,27654,27656],{},[84,27653,20410],{},[102,27655,820],{},[397,27657,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,27659,27660],{"encoding":108},"c_1'",[60,27662,27664],{"className":27663,"ariaHidden":114},[113],[60,27665,27667,27670],{"className":27666},[118],[60,27668],{"className":27669,"style":17392},[122],[60,27671,27673,27676],{"className":27672},[127],[60,27674,20410],{"className":27675},[127,178],[60,27677,27679],{"className":27678},[183],[60,27680,27682,27716],{"className":27681},[139,140],[60,27683,27685,27713],{"className":27684},[144],[60,27686,27688,27699],{"className":27687,"style":605},[148],[60,27689,27690,27693],{"style":17413},[60,27691],{"className":27692,"style":325},[156],[60,27694,27696],{"className":27695},[161,162,163,164],[60,27697,820],{"className":27698},[127,164],[60,27700,27701,27704],{"style":608},[60,27702],{"className":27703,"style":325},[156],[60,27705,27707],{"className":27706},[161,162,163,164],[60,27708,27710],{"className":27709},[127,164],[60,27711,557],{"className":27712},[127,164],[60,27714,213],{"className":27715},[212],[60,27717,27719],{"className":27718},[144],[60,27720,27722],{"className":27721,"style":17446},[148],[60,27723],{},[60,27725,27727,27813],{"className":27726},[63],[60,27728,27730],{"className":27729},[67],[69,27731,27732],{"xmlns":71},[73,27733,27734,27810],{},[76,27735,27736,27744,27746,27748,27758,27760,27762,27764,27766,27776,27778,27780,27782,27784,27786,27788,27790,27792,27794,27796,27798,27800,27802,27804,27806,27808],{},[2127,27737,27738,27740,27742],{},[84,27739,20410],{},[102,27741,814],{},[397,27743,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,27745,400],{"stretchy":399},[102,27747,814],{},[550,27749,27750,27756],{},[76,27751,27752,27754],{},[84,27753,9061],{},[397,27755,1465],{},[102,27757,814],{},[102,27759,814],{},[84,27761,2152],{},[397,27763,990],{},[102,27765,814],{},[550,27767,27768,27774],{},[76,27769,27770,27772],{},[84,27771,11088],{},[397,27773,1465],{},[102,27775,814],{},[102,27777,814],{},[84,27779,2152],{},[397,27781,405],{"stretchy":399},[397,27783,448],{},[397,27785,400],{"stretchy":399},[84,27787,2152],{},[84,27789,9061],{},[397,27791,1465],{},[102,27793,814],{},[84,27795,2152],{},[397,27797,405],{"stretchy":399},[397,27799,400],{"stretchy":399},[84,27801,11088],{},[397,27803,1465],{},[102,27805,814],{},[84,27807,2152],{},[397,27809,405],{"stretchy":399},[106,27811,27812],{"encoding":108},"c_2'(2\\sin^2 2t + 2\\cos^2 2t) = (t\\sin 2t)(\\cos 2t)",[60,27814,27816,27935,27997],{"className":27815,"ariaHidden":114},[113],[60,27817,27819,27823,27877,27880,27883,27886,27917,27920,27923,27926,27929,27932],{"className":27818},[118],[60,27820],{"className":27821,"style":27822},[122],"height:1.1219em;vertical-align:-0.25em;",[60,27824,27826,27829],{"className":27825},[127],[60,27827,20410],{"className":27828},[127,178],[60,27830,27832],{"className":27831},[183],[60,27833,27835,27869],{"className":27834},[139,140],[60,27836,27838,27866],{"className":27837},[144],[60,27839,27841,27852],{"className":27840,"style":605},[148],[60,27842,27843,27846],{"style":17413},[60,27844],{"className":27845,"style":325},[156],[60,27847,27849],{"className":27848},[161,162,163,164],[60,27850,814],{"className":27851},[127,164],[60,27853,27854,27857],{"style":608},[60,27855],{"className":27856,"style":325},[156],[60,27858,27860],{"className":27859},[161,162,163,164],[60,27861,27863],{"className":27862},[127,164],[60,27864,557],{"className":27865},[127,164],[60,27867,213],{"className":27868},[212],[60,27870,27872],{"className":27871},[144],[60,27873,27875],{"className":27874,"style":17446},[148],[60,27876],{},[60,27878,400],{"className":27879},[131],[60,27881,814],{"className":27882},[127],[60,27884],{"className":27885,"style":653},[469],[60,27887,27889,27892],{"className":27888},[1495],[60,27890,9061],{"className":27891},[1495],[60,27893,27895],{"className":27894},[183],[60,27896,27898],{"className":27897},[139],[60,27899,27901],{"className":27900},[144],[60,27902,27905],{"className":27903,"style":27904},[148],"height:0.8719em;",[60,27906,27908,27911],{"style":27907},"top:-3.1208em;margin-right:0.05em;",[60,27909],{"className":27910,"style":325},[156],[60,27912,27914],{"className":27913},[161,162,163,164],[60,27915,814],{"className":27916},[127,164],[60,27918],{"className":27919,"style":653},[469],[60,27921,814],{"className":27922},[127],[60,27924,2152],{"className":27925},[127,178],[60,27927],{"className":27928,"style":924},[469],[60,27930,990],{"className":27931},[928],[60,27933],{"className":27934,"style":924},[469],[60,27936,27938,27941,27944,27947,27976,27979,27982,27985,27988,27991,27994],{"className":27937},[118],[60,27939],{"className":27940,"style":887},[122],[60,27942,814],{"className":27943},[127],[60,27945],{"className":27946,"style":653},[469],[60,27948,27950,27953],{"className":27949},[1495],[60,27951,11088],{"className":27952},[1495],[60,27954,27956],{"className":27955},[183],[60,27957,27959],{"className":27958},[139],[60,27960,27962],{"className":27961},[144],[60,27963,27965],{"className":27964,"style":909},[148],[60,27966,27967,27970],{"style":608},[60,27968],{"className":27969,"style":325},[156],[60,27971,27973],{"className":27972},[161,162,163,164],[60,27974,814],{"className":27975},[127,164],[60,27977],{"className":27978,"style":653},[469],[60,27980,814],{"className":27981},[127],[60,27983,2152],{"className":27984},[127,178],[60,27986,405],{"className":27987},[267],[60,27989],{"className":27990,"style":470},[469],[60,27992,448],{"className":27993},[474],[60,27995],{"className":27996,"style":470},[469],[60,27998,28000,28003,28006,28009,28012,28015,28018,28021,28024,28027,28030,28033,28036,28039,28042],{"className":27999},[118],[60,28001],{"className":28002,"style":418},[122],[60,28004,400],{"className":28005},[131],[60,28007,2152],{"className":28008},[127,178],[60,28010],{"className":28011,"style":653},[469],[60,28013,9061],{"className":28014},[1495],[60,28016],{"className":28017,"style":653},[469],[60,28019,814],{"className":28020},[127],[60,28022,2152],{"className":28023},[127,178],[60,28025,405],{"className":28026},[267],[60,28028,400],{"className":28029},[131],[60,28031,11088],{"className":28032},[1495],[60,28034],{"className":28035,"style":653},[469],[60,28037,814],{"className":28038},[127],[60,28040,2152],{"className":28041},[127,178],[60,28043,405],{"className":28044},[267],[60,28046,28048,28108],{"className":28047},[63],[60,28049,28051],{"className":28050},[67],[69,28052,28053],{"xmlns":71},[73,28054,28055,28105],{},[76,28056,28057,28059,28067,28069,28071,28073,28075,28077,28079,28081,28083,28085,28087,28089,28095,28097,28099,28101,28103],{},[102,28058,814],{},[2127,28060,28061,28063,28065],{},[84,28062,20410],{},[102,28064,814],{},[397,28066,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,28068,448],{},[84,28070,2152],{},[84,28072,9061],{},[397,28074,1465],{},[102,28076,814],{},[84,28078,2152],{},[84,28080,11088],{},[397,28082,1465],{},[102,28084,814],{},[84,28086,2152],{},[397,28088,448],{},[79,28090,28091,28093],{},[102,28092,820],{},[102,28094,814],{},[84,28096,2152],{},[84,28098,9061],{},[397,28100,1465],{},[102,28102,23145],{},[84,28104,2152],{},[106,28106,28107],{"encoding":108},"2c_2' = t\\sin 2t \\cos 2t = \\frac{1}{2}t \\sin 4t",[60,28109,28111,28183,28231],{"className":28110,"ariaHidden":114},[113],[60,28112,28114,28117,28120,28174,28177,28180],{"className":28113},[118],[60,28115],{"className":28116,"style":17392},[122],[60,28118,814],{"className":28119},[127],[60,28121,28123,28126],{"className":28122},[127],[60,28124,20410],{"className":28125},[127,178],[60,28127,28129],{"className":28128},[183],[60,28130,28132,28166],{"className":28131},[139,140],[60,28133,28135,28163],{"className":28134},[144],[60,28136,28138,28149],{"className":28137,"style":605},[148],[60,28139,28140,28143],{"style":17413},[60,28141],{"className":28142,"style":325},[156],[60,28144,28146],{"className":28145},[161,162,163,164],[60,28147,814],{"className":28148},[127,164],[60,28150,28151,28154],{"style":608},[60,28152],{"className":28153,"style":325},[156],[60,28155,28157],{"className":28156},[161,162,163,164],[60,28158,28160],{"className":28159},[127,164],[60,28161,557],{"className":28162},[127,164],[60,28164,213],{"className":28165},[212],[60,28167,28169],{"className":28168},[144],[60,28170,28172],{"className":28171,"style":17446},[148],[60,28173],{},[60,28175],{"className":28176,"style":470},[469],[60,28178,448],{"className":28179},[474],[60,28181],{"className":28182,"style":470},[469],[60,28184,28186,28189,28192,28195,28198,28201,28204,28207,28210,28213,28216,28219,28222,28225,28228],{"className":28185},[118],[60,28187],{"className":28188,"style":26595},[122],[60,28190,2152],{"className":28191},[127,178],[60,28193],{"className":28194,"style":653},[469],[60,28196,9061],{"className":28197},[1495],[60,28199],{"className":28200,"style":653},[469],[60,28202,814],{"className":28203},[127],[60,28205,2152],{"className":28206},[127,178],[60,28208],{"className":28209,"style":653},[469],[60,28211,11088],{"className":28212},[1495],[60,28214],{"className":28215,"style":653},[469],[60,28217,814],{"className":28218},[127],[60,28220,2152],{"className":28221},[127,178],[60,28223],{"className":28224,"style":470},[469],[60,28226,448],{"className":28227},[474],[60,28229],{"className":28230,"style":470},[469],[60,28232,28234,28237,28305,28308,28311,28314,28317,28320],{"className":28233},[118],[60,28235],{"className":28236,"style":12028},[122],[60,28238,28240,28243,28302],{"className":28239},[127],[60,28241],{"className":28242},[131,132],[60,28244,28246],{"className":28245},[79],[60,28247,28249,28294],{"className":28248},[139,140],[60,28250,28252,28291],{"className":28251},[144],[60,28253,28255,28269,28277],{"className":28254,"style":11547},[148],[60,28256,28257,28260],{"style":152},[60,28258],{"className":28259,"style":157},[156],[60,28261,28263],{"className":28262},[161,162,163,164],[60,28264,28266],{"className":28265},[127,164],[60,28267,814],{"className":28268},[127,164],[60,28270,28271,28274],{"style":225},[60,28272],{"className":28273,"style":157},[156],[60,28275],{"className":28276,"style":233},[232],[60,28278,28279,28282],{"style":1105},[60,28280],{"className":28281,"style":157},[156],[60,28283,28285],{"className":28284},[161,162,163,164],[60,28286,28288],{"className":28287},[127,164],[60,28289,820],{"className":28290},[127,164],[60,28292,213],{"className":28293},[212],[60,28295,28297],{"className":28296},[144],[60,28298,28300],{"className":28299,"style":3907},[148],[60,28301],{},[60,28303],{"className":28304},[267,132],[60,28306,2152],{"className":28307},[127,178],[60,28309],{"className":28310,"style":653},[469],[60,28312,9061],{"className":28313},[1495],[60,28315],{"className":28316,"style":653},[469],[60,28318,23145],{"className":28319},[127],[60,28321,2152],{"className":28322},[127,178],[60,28324,28326,28370],{"className":28325},[63],[60,28327,28329],{"className":28328},[67],[69,28330,28331],{"xmlns":71},[73,28332,28333,28367],{},[76,28334,28335,28337,28339,28341,28349,28351,28357,28359,28361,28363,28365],{},[13095,28336,18294],{},[397,28338,18297],{},[13095,28340,18294],{},[2127,28342,28343,28345,28347],{},[84,28344,20410],{},[102,28346,814],{},[397,28348,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,28350,448],{},[79,28352,28353,28355],{},[102,28354,820],{},[102,28356,23145],{},[84,28358,2152],{},[84,28360,9061],{},[397,28362,1465],{},[102,28364,23145],{},[84,28366,2152],{},[106,28368,28369],{"encoding":108},"\\implies c_2' = \\frac{1}{4}t \\sin 4t",[60,28371,28373,28391,28460],{"className":28372,"ariaHidden":114},[113],[60,28374,28376,28379,28382,28385,28388],{"className":28375},[118],[60,28377],{"className":28378,"style":18338},[122],[60,28380],{"className":28381,"style":470},[469],[60,28383,18297],{"className":28384},[474],[60,28386],{"className":28387,"style":470},[469],[60,28389],{"className":28390,"style":470},[469],[60,28392,28394,28397,28451,28454,28457],{"className":28393},[118],[60,28395],{"className":28396,"style":17392},[122],[60,28398,28400,28403],{"className":28399},[127],[60,28401,20410],{"className":28402},[127,178],[60,28404,28406],{"className":28405},[183],[60,28407,28409,28443],{"className":28408},[139,140],[60,28410,28412,28440],{"className":28411},[144],[60,28413,28415,28426],{"className":28414,"style":605},[148],[60,28416,28417,28420],{"style":17413},[60,28418],{"className":28419,"style":325},[156],[60,28421,28423],{"className":28422},[161,162,163,164],[60,28424,814],{"className":28425},[127,164],[60,28427,28428,28431],{"style":608},[60,28429],{"className":28430,"style":325},[156],[60,28432,28434],{"className":28433},[161,162,163,164],[60,28435,28437],{"className":28436},[127,164],[60,28438,557],{"className":28439},[127,164],[60,28441,213],{"className":28442},[212],[60,28444,28446],{"className":28445},[144],[60,28447,28449],{"className":28448,"style":17446},[148],[60,28450],{},[60,28452],{"className":28453,"style":470},[469],[60,28455,448],{"className":28456},[474],[60,28458],{"className":28459,"style":470},[469],[60,28461,28463,28466,28534,28537,28540,28543,28546,28549],{"className":28462},[118],[60,28464],{"className":28465,"style":12028},[122],[60,28467,28469,28472,28531],{"className":28468},[127],[60,28470],{"className":28471},[131,132],[60,28473,28475],{"className":28474},[79],[60,28476,28478,28523],{"className":28477},[139,140],[60,28479,28481,28520],{"className":28480},[144],[60,28482,28484,28498,28506],{"className":28483,"style":11547},[148],[60,28485,28486,28489],{"style":152},[60,28487],{"className":28488,"style":157},[156],[60,28490,28492],{"className":28491},[161,162,163,164],[60,28493,28495],{"className":28494},[127,164],[60,28496,23145],{"className":28497},[127,164],[60,28499,28500,28503],{"style":225},[60,28501],{"className":28502,"style":157},[156],[60,28504],{"className":28505,"style":233},[232],[60,28507,28508,28511],{"style":1105},[60,28509],{"className":28510,"style":157},[156],[60,28512,28514],{"className":28513},[161,162,163,164],[60,28515,28517],{"className":28516},[127,164],[60,28518,820],{"className":28519},[127,164],[60,28521,213],{"className":28522},[212],[60,28524,28526],{"className":28525},[144],[60,28527,28529],{"className":28528,"style":3907},[148],[60,28530],{},[60,28532],{"className":28533},[267,132],[60,28535,2152],{"className":28536},[127,178],[60,28538],{"className":28539,"style":653},[469],[60,28541,9061],{"className":28542},[1495],[60,28544],{"className":28545,"style":653},[469],[60,28547,23145],{"className":28548},[127],[60,28550,2152],{"className":28551},[127,178],[33,28553,28554,28555,28640,28641,29346,29347,29550,29551],{},"求 ",[60,28556,28558,28577],{"className":28557},[63],[60,28559,28561],{"className":28560},[67],[69,28562,28563],{"xmlns":71},[73,28564,28565,28575],{},[76,28566,28567],{},[2127,28568,28569,28571,28573],{},[84,28570,20410],{},[102,28572,820],{},[397,28574,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,28576,27660],{"encoding":108},[60,28578,28580],{"className":28579,"ariaHidden":114},[113],[60,28581,28583,28586],{"className":28582},[118],[60,28584],{"className":28585,"style":17392},[122],[60,28587,28589,28592],{"className":28588},[127],[60,28590,20410],{"className":28591},[127,178],[60,28593,28595],{"className":28594},[183],[60,28596,28598,28632],{"className":28597},[139,140],[60,28599,28601,28629],{"className":28600},[144],[60,28602,28604,28615],{"className":28603,"style":605},[148],[60,28605,28606,28609],{"style":17413},[60,28607],{"className":28608,"style":325},[156],[60,28610,28612],{"className":28611},[161,162,163,164],[60,28613,820],{"className":28614},[127,164],[60,28616,28617,28620],{"style":608},[60,28618],{"className":28619,"style":325},[156],[60,28621,28623],{"className":28622},[161,162,163,164],[60,28624,28626],{"className":28625},[127,164],[60,28627,557],{"className":28628},[127,164],[60,28630,213],{"className":28631},[212],[60,28633,28635],{"className":28634},[144],[60,28636,28638],{"className":28637,"style":17446},[148],[60,28639],{},"：由第一式 ",[60,28642,28644,28766],{"className":28643},[63],[60,28645,28647],{"className":28646},[67],[69,28648,28649],{"xmlns":71},[73,28650,28651,28763],{},[76,28652,28653,28661,28663,28665,28673,28695,28697,28699,28705,28707,28709,28711,28713,28715,28737,28739,28741,28747,28749,28759,28761],{},[2127,28654,28655,28657,28659],{},[84,28656,20410],{},[102,28658,820],{},[397,28660,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,28662,448],{},[397,28664,817],{},[2127,28666,28667,28669,28671],{},[84,28668,20410],{},[102,28670,814],{},[397,28672,557],{"mathvariant":86,"lspace":556,"rspace":556},[79,28674,28675,28685],{},[76,28676,28677,28679,28681,28683],{},[84,28678,9061],{},[397,28680,1465],{},[102,28682,814],{},[84,28684,2152],{},[76,28686,28687,28689,28691,28693],{},[84,28688,11088],{},[397,28690,1465],{},[102,28692,814],{},[84,28694,2152],{},[397,28696,448],{},[397,28698,817],{},[79,28700,28701,28703],{},[102,28702,820],{},[102,28704,23145],{},[84,28706,2152],{},[84,28708,9061],{},[397,28710,1465],{},[102,28712,23145],{},[84,28714,2152],{},[79,28716,28717,28727],{},[76,28718,28719,28721,28723,28725],{},[84,28720,9061],{},[397,28722,1465],{},[102,28724,814],{},[84,28726,2152],{},[76,28728,28729,28731,28733,28735],{},[84,28730,11088],{},[397,28732,1465],{},[102,28734,814],{},[84,28736,2152],{},[397,28738,448],{},[397,28740,817],{},[79,28742,28743,28745],{},[102,28744,820],{},[102,28746,814],{},[84,28748,2152],{},[550,28750,28751,28757],{},[76,28752,28753,28755],{},[84,28754,9061],{},[397,28756,1465],{},[102,28758,814],{},[102,28760,814],{},[84,28762,2152],{},[106,28764,28765],{"encoding":108},"c_1' = -c_2' \\frac{\\sin 2t}{\\cos 2t} = -\\frac{1}{4}t \\sin 4t \\frac{\\sin 2t}{\\cos 2t} = -\\frac{1}{2}t \\sin^2 2t",[60,28767,28769,28838,29016,29224],{"className":28768,"ariaHidden":114},[113],[60,28770,28772,28775,28829,28832,28835],{"className":28771},[118],[60,28773],{"className":28774,"style":17392},[122],[60,28776,28778,28781],{"className":28777},[127],[60,28779,20410],{"className":28780},[127,178],[60,28782,28784],{"className":28783},[183],[60,28785,28787,28821],{"className":28786},[139,140],[60,28788,28790,28818],{"className":28789},[144],[60,28791,28793,28804],{"className":28792,"style":605},[148],[60,28794,28795,28798],{"style":17413},[60,28796],{"className":28797,"style":325},[156],[60,28799,28801],{"className":28800},[161,162,163,164],[60,28802,820],{"className":28803},[127,164],[60,28805,28806,28809],{"style":608},[60,28807],{"className":28808,"style":325},[156],[60,28810,28812],{"className":28811},[161,162,163,164],[60,28813,28815],{"className":28814},[127,164],[60,28816,557],{"className":28817},[127,164],[60,28819,213],{"className":28820},[212],[60,28822,28824],{"className":28823},[144],[60,28825,28827],{"className":28826,"style":17446},[148],[60,28828],{},[60,28830],{"className":28831,"style":470},[469],[60,28833,448],{"className":28834},[474],[60,28836],{"className":28837,"style":470},[469],[60,28839,28841,28845,28848,28902,29007,29010,29013],{"className":28840},[118],[60,28842],{"className":28843,"style":28844},[122],"height:1.2065em;vertical-align:-0.345em;",[60,28846,817],{"className":28847},[127],[60,28849,28851,28854],{"className":28850},[127],[60,28852,20410],{"className":28853},[127,178],[60,28855,28857],{"className":28856},[183],[60,28858,28860,28894],{"className":28859},[139,140],[60,28861,28863,28891],{"className":28862},[144],[60,28864,28866,28877],{"className":28865,"style":605},[148],[60,28867,28868,28871],{"style":17413},[60,28869],{"className":28870,"style":325},[156],[60,28872,28874],{"className":28873},[161,162,163,164],[60,28875,814],{"className":28876},[127,164],[60,28878,28879,28882],{"style":608},[60,28880],{"className":28881,"style":325},[156],[60,28883,28885],{"className":28884},[161,162,163,164],[60,28886,28888],{"className":28887},[127,164],[60,28889,557],{"className":28890},[127,164],[60,28892,213],{"className":28893},[212],[60,28895,28897],{"className":28896},[144],[60,28898,28900],{"className":28899,"style":17446},[148],[60,28901],{},[60,28903,28905,28908,29004],{"className":28904},[127],[60,28906],{"className":28907},[131,132],[60,28909,28911],{"className":28910},[79],[60,28912,28914,28996],{"className":28913},[139,140],[60,28915,28917,28993],{"className":28916},[144],[60,28918,28921,28953,28961],{"className":28919,"style":28920},[148],"height:0.8615em;",[60,28922,28923,28926],{"style":152},[60,28924],{"className":28925,"style":157},[156],[60,28927,28929],{"className":28928},[161,162,163,164],[60,28930,28932,28944,28947,28950],{"className":28931},[127,164],[60,28933,28935,28938,28941],{"className":28934},[1495,164],[60,28936,20410],{"className":28937},[164],[60,28939,22982],{"className":28940},[164],[60,28942,22986],{"className":28943},[164],[60,28945],{"className":28946,"style":22972},[469,164],[60,28948,814],{"className":28949},[127,164],[60,28951,2152],{"className":28952},[127,178,164],[60,28954,28955,28958],{"style":225},[60,28956],{"className":28957,"style":157},[156],[60,28959],{"className":28960,"style":233},[232],[60,28962,28963,28966],{"style":1105},[60,28964],{"className":28965,"style":157},[156],[60,28967,28969],{"className":28968},[161,162,163,164],[60,28970,28972,28984,28987,28990],{"className":28971},[127,164],[60,28973,28975,28978,28981],{"className":28974},[1495,164],[60,28976,22986],{"className":28977},[164],[60,28979,23005],{"className":28980},[164],[60,28982,16342],{"className":28983},[164],[60,28985],{"className":28986,"style":22972},[469,164],[60,28988,814],{"className":28989},[127,164],[60,28991,2152],{"className":28992},[127,178,164],[60,28994,213],{"className":28995},[212],[60,28997,28999],{"className":28998},[144],[60,29000,29002],{"className":29001,"style":3907},[148],[60,29003],{},[60,29005],{"className":29006},[267,132],[60,29008],{"className":29009,"style":470},[469],[60,29011,448],{"className":29012},[474],[60,29014],{"className":29015,"style":470},[469],[60,29017,29019,29022,29025,29093,29096,29099,29102,29105,29108,29111,29215,29218,29221],{"className":29018},[118],[60,29020],{"className":29021,"style":28844},[122],[60,29023,817],{"className":29024},[127],[60,29026,29028,29031,29090],{"className":29027},[127],[60,29029],{"className":29030},[131,132],[60,29032,29034],{"className":29033},[79],[60,29035,29037,29082],{"className":29036},[139,140],[60,29038,29040,29079],{"className":29039},[144],[60,29041,29043,29057,29065],{"className":29042,"style":11547},[148],[60,29044,29045,29048],{"style":152},[60,29046],{"className":29047,"style":157},[156],[60,29049,29051],{"className":29050},[161,162,163,164],[60,29052,29054],{"className":29053},[127,164],[60,29055,23145],{"className":29056},[127,164],[60,29058,29059,29062],{"style":225},[60,29060],{"className":29061,"style":157},[156],[60,29063],{"className":29064,"style":233},[232],[60,29066,29067,29070],{"style":1105},[60,29068],{"className":29069,"style":157},[156],[60,29071,29073],{"className":29072},[161,162,163,164],[60,29074,29076],{"className":29075},[127,164],[60,29077,820],{"className":29078},[127,164],[60,29080,213],{"className":29081},[212],[60,29083,29085],{"className":29084},[144],[60,29086,29088],{"className":29087,"style":3907},[148],[60,29089],{},[60,29091],{"className":29092},[267,132],[60,29094,2152],{"className":29095},[127,178],[60,29097],{"className":29098,"style":653},[469],[60,29100,9061],{"className":29101},[1495],[60,29103],{"className":29104,"style":653},[469],[60,29106,23145],{"className":29107},[127],[60,29109,2152],{"className":29110},[127,178],[60,29112,29114,29117,29212],{"className":29113},[127],[60,29115],{"className":29116},[131,132],[60,29118,29120],{"className":29119},[79],[60,29121,29123,29204],{"className":29122},[139,140],[60,29124,29126,29201],{"className":29125},[144],[60,29127,29129,29161,29169],{"className":29128,"style":28920},[148],[60,29130,29131,29134],{"style":152},[60,29132],{"className":29133,"style":157},[156],[60,29135,29137],{"className":29136},[161,162,163,164],[60,29138,29140,29152,29155,29158],{"className":29139},[127,164],[60,29141,29143,29146,29149],{"className":29142},[1495,164],[60,29144,20410],{"className":29145},[164],[60,29147,22982],{"className":29148},[164],[60,29150,22986],{"className":29151},[164],[60,29153],{"className":29154,"style":22972},[469,164],[60,29156,814],{"className":29157},[127,164],[60,29159,2152],{"className":29160},[127,178,164],[60,29162,29163,29166],{"style":225},[60,29164],{"className":29165,"style":157},[156],[60,29167],{"className":29168,"style":233},[232],[60,29170,29171,29174],{"style":1105},[60,29172],{"className":29173,"style":157},[156],[60,29175,29177],{"className":29176},[161,162,163,164],[60,29178,29180,29192,29195,29198],{"className":29179},[127,164],[60,29181,29183,29186,29189],{"className":29182},[1495,164],[60,29184,22986],{"className":29185},[164],[60,29187,23005],{"className":29188},[164],[60,29190,16342],{"className":29191},[164],[60,29193],{"className":29194,"style":22972},[469,164],[60,29196,814],{"className":29197},[127,164],[60,29199,2152],{"className":29200},[127,178,164],[60,29202,213],{"className":29203},[212],[60,29205,29207],{"className":29206},[144],[60,29208,29210],{"className":29209,"style":3907},[148],[60,29211],{},[60,29213],{"className":29214},[267,132],[60,29216],{"className":29217,"style":470},[469],[60,29219,448],{"className":29220},[474],[60,29222],{"className":29223,"style":470},[469],[60,29225,29227,29231,29234,29302,29305,29308,29337,29340,29343],{"className":29226},[118],[60,29228],{"className":29229,"style":29230},[122],"height:1.2169em;vertical-align:-0.345em;",[60,29232,817],{"className":29233},[127],[60,29235,29237,29240,29299],{"className":29236},[127],[60,29238],{"className":29239},[131,132],[60,29241,29243],{"className":29242},[79],[60,29244,29246,29291],{"className":29245},[139,140],[60,29247,29249,29288],{"className":29248},[144],[60,29250,29252,29266,29274],{"className":29251,"style":11547},[148],[60,29253,29254,29257],{"style":152},[60,29255],{"className":29256,"style":157},[156],[60,29258,29260],{"className":29259},[161,162,163,164],[60,29261,29263],{"className":29262},[127,164],[60,29264,814],{"className":29265},[127,164],[60,29267,29268,29271],{"style":225},[60,29269],{"className":29270,"style":157},[156],[60,29272],{"className":29273,"style":233},[232],[60,29275,29276,29279],{"style":1105},[60,29277],{"className":29278,"style":157},[156],[60,29280,29282],{"className":29281},[161,162,163,164],[60,29283,29285],{"className":29284},[127,164],[60,29286,820],{"className":29287},[127,164],[60,29289,213],{"className":29290},[212],[60,29292,29294],{"className":29293},[144],[60,29295,29297],{"className":29296,"style":3907},[148],[60,29298],{},[60,29300],{"className":29301},[267,132],[60,29303,2152],{"className":29304},[127,178],[60,29306],{"className":29307,"style":653},[469],[60,29309,29311,29314],{"className":29310},[1495],[60,29312,9061],{"className":29313},[1495],[60,29315,29317],{"className":29316},[183],[60,29318,29320],{"className":29319},[139],[60,29321,29323],{"className":29322},[144],[60,29324,29326],{"className":29325,"style":27904},[148],[60,29327,29328,29331],{"style":27907},[60,29329],{"className":29330,"style":325},[156],[60,29332,29334],{"className":29333},[161,162,163,164],[60,29335,814],{"className":29336},[127,164],[60,29338],{"className":29339,"style":653},[469],[60,29341,814],{"className":29342},[127],[60,29344,2152],{"className":29345},[127,178],"\n(利用三角公式降幂：",[60,29348,29350,29396],{"className":29349},[63],[60,29351,29353],{"className":29352},[67],[69,29354,29355],{"xmlns":71},[73,29356,29357,29393],{},[76,29358,29359,29369,29371,29373,29375],{},[550,29360,29361,29367],{},[76,29362,29363,29365],{},[84,29364,9061],{},[397,29366,1465],{},[102,29368,814],{},[102,29370,814],{},[84,29372,2152],{},[397,29374,448],{},[79,29376,29377,29391],{},[76,29378,29379,29381,29383,29385,29387,29389],{},[102,29380,820],{},[397,29382,817],{},[84,29384,11088],{},[397,29386,1465],{},[102,29388,23145],{},[84,29390,2152],{},[102,29392,814],{},[106,29394,29395],{"encoding":108},"\\sin^2 2t = \\frac{1-\\cos 4t}{2}",[60,29397,29399,29452],{"className":29398,"ariaHidden":114},[113],[60,29400,29402,29405,29434,29437,29440,29443,29446,29449],{"className":29401},[118],[60,29403],{"className":29404,"style":27904},[122],[60,29406,29408,29411],{"className":29407},[1495],[60,29409,9061],{"className":29410},[1495],[60,29412,29414],{"className":29413},[183],[60,29415,29417],{"className":29416},[139],[60,29418,29420],{"className":29419},[144],[60,29421,29423],{"className":29422,"style":27904},[148],[60,29424,29425,29428],{"style":27907},[60,29426],{"className":29427,"style":325},[156],[60,29429,29431],{"className":29430},[161,162,163,164],[60,29432,814],{"className":29433},[127,164],[60,29435],{"className":29436,"style":653},[469],[60,29438,814],{"className":29439},[127],[60,29441,2152],{"className":29442},[127,178],[60,29444],{"className":29445,"style":470},[469],[60,29447,448],{"className":29448},[474],[60,29450],{"className":29451,"style":470},[469],[60,29453,29455,29458],{"className":29454},[118],[60,29456],{"className":29457,"style":12028},[122],[60,29459,29461,29464,29547],{"className":29460},[127],[60,29462],{"className":29463},[131,132],[60,29465,29467],{"className":29466},[79],[60,29468,29470,29539],{"className":29469},[139,140],[60,29471,29473,29536],{"className":29472},[144],[60,29474,29476,29490,29498],{"className":29475,"style":11547},[148],[60,29477,29478,29481],{"style":152},[60,29479],{"className":29480,"style":157},[156],[60,29482,29484],{"className":29483},[161,162,163,164],[60,29485,29487],{"className":29486},[127,164],[60,29488,814],{"className":29489},[127,164],[60,29491,29492,29495],{"style":225},[60,29493],{"className":29494,"style":157},[156],[60,29496],{"className":29497,"style":233},[232],[60,29499,29500,29503],{"style":1105},[60,29501],{"className":29502,"style":157},[156],[60,29504,29506],{"className":29505},[161,162,163,164],[60,29507,29509,29512,29515,29527,29530,29533],{"className":29508},[127,164],[60,29510,820],{"className":29511},[127,164],[60,29513,817],{"className":29514},[928,164],[60,29516,29518,29521,29524],{"className":29517},[1495,164],[60,29519,20410],{"className":29520},[164],[60,29522,22982],{"className":29523},[164],[60,29525,22986],{"className":29526},[164],[60,29528],{"className":29529,"style":22972},[469,164],[60,29531,23145],{"className":29532},[127,164],[60,29534,2152],{"className":29535},[127,178,164],[60,29537,213],{"className":29538},[212],[60,29540,29542],{"className":29541},[144],[60,29543,29545],{"className":29544,"style":3907},[148],[60,29546],{},[60,29548],{"className":29549},[267,132],")\n",[60,29552,29554,29638],{"className":29553},[63],[60,29555,29557],{"className":29556},[67],[69,29558,29559],{"xmlns":71},[73,29560,29561,29635],{},[76,29562,29563,29565,29567,29569,29577,29579,29581,29587,29589,29591,29593,29595,29597,29599,29601,29603,29605,29607,29609,29615,29617,29619,29625,29627,29629,29631,29633],{},[13095,29564,18294],{},[397,29566,18297],{},[13095,29568,18294],{},[2127,29570,29571,29573,29575],{},[84,29572,20410],{},[102,29574,820],{},[397,29576,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,29578,448],{},[397,29580,817],{},[79,29582,29583,29585],{},[102,29584,820],{},[102,29586,23145],{},[84,29588,2152],{},[397,29590,400],{"stretchy":399},[102,29592,820],{},[397,29594,817],{},[84,29596,11088],{},[397,29598,1465],{},[102,29600,23145],{},[84,29602,2152],{},[397,29604,405],{"stretchy":399},[397,29606,448],{},[397,29608,817],{},[79,29610,29611,29613],{},[102,29612,820],{},[102,29614,23145],{},[84,29616,2152],{},[397,29618,990],{},[79,29620,29621,29623],{},[102,29622,820],{},[102,29624,23145],{},[84,29626,2152],{},[84,29628,11088],{},[397,29630,1465],{},[102,29632,23145],{},[84,29634,2152],{},[106,29636,29637],{"encoding":108},"\\implies c_1' = -\\frac{1}{4}t(1-\\cos 4t) = -\\frac{1}{4}t + \\frac{1}{4}t \\cos 4t",[60,29639,29641,29659,29728,29823,29853,29942],{"className":29640,"ariaHidden":114},[113],[60,29642,29644,29647,29650,29653,29656],{"className":29643},[118],[60,29645],{"className":29646,"style":18338},[122],[60,29648],{"className":29649,"style":470},[469],[60,29651,18297],{"className":29652},[474],[60,29654],{"className":29655,"style":470},[469],[60,29657],{"className":29658,"style":470},[469],[60,29660,29662,29665,29719,29722,29725],{"className":29661},[118],[60,29663],{"className":29664,"style":17392},[122],[60,29666,29668,29671],{"className":29667},[127],[60,29669,20410],{"className":29670},[127,178],[60,29672,29674],{"className":29673},[183],[60,29675,29677,29711],{"className":29676},[139,140],[60,29678,29680,29708],{"className":29679},[144],[60,29681,29683,29694],{"className":29682,"style":605},[148],[60,29684,29685,29688],{"style":17413},[60,29686],{"className":29687,"style":325},[156],[60,29689,29691],{"className":29690},[161,162,163,164],[60,29692,820],{"className":29693},[127,164],[60,29695,29696,29699],{"style":608},[60,29697],{"className":29698,"style":325},[156],[60,29700,29702],{"className":29701},[161,162,163,164],[60,29703,29705],{"className":29704},[127,164],[60,29706,557],{"className":29707},[127,164],[60,29709,213],{"className":29710},[212],[60,29712,29714],{"className":29713},[144],[60,29715,29717],{"className":29716,"style":17446},[148],[60,29718],{},[60,29720],{"className":29721,"style":470},[469],[60,29723,448],{"className":29724},[474],[60,29726],{"className":29727,"style":470},[469],[60,29729,29731,29734,29737,29805,29808,29811,29814,29817,29820],{"className":29730},[118],[60,29732],{"className":29733,"style":12028},[122],[60,29735,817],{"className":29736},[127],[60,29738,29740,29743,29802],{"className":29739},[127],[60,29741],{"className":29742},[131,132],[60,29744,29746],{"className":29745},[79],[60,29747,29749,29794],{"className":29748},[139,140],[60,29750,29752,29791],{"className":29751},[144],[60,29753,29755,29769,29777],{"className":29754,"style":11547},[148],[60,29756,29757,29760],{"style":152},[60,29758],{"className":29759,"style":157},[156],[60,29761,29763],{"className":29762},[161,162,163,164],[60,29764,29766],{"className":29765},[127,164],[60,29767,23145],{"className":29768},[127,164],[60,29770,29771,29774],{"style":225},[60,29772],{"className":29773,"style":157},[156],[60,29775],{"className":29776,"style":233},[232],[60,29778,29779,29782],{"style":1105},[60,29780],{"className":29781,"style":157},[156],[60,29783,29785],{"className":29784},[161,162,163,164],[60,29786,29788],{"className":29787},[127,164],[60,29789,820],{"className":29790},[127,164],[60,29792,213],{"className":29793},[212],[60,29795,29797],{"className":29796},[144],[60,29798,29800],{"className":29799,"style":3907},[148],[60,29801],{},[60,29803],{"className":29804},[267,132],[60,29806,2152],{"className":29807},[127,178],[60,29809,400],{"className":29810},[131],[60,29812,820],{"className":29813},[127],[60,29815],{"className":29816,"style":924},[469],[60,29818,817],{"className":29819},[928],[60,29821],{"className":29822,"style":924},[469],[60,29824,29826,29829,29832,29835,29838,29841,29844,29847,29850],{"className":29825},[118],[60,29827],{"className":29828,"style":418},[122],[60,29830,11088],{"className":29831},[1495],[60,29833],{"className":29834,"style":653},[469],[60,29836,23145],{"className":29837},[127],[60,29839,2152],{"className":29840},[127,178],[60,29842,405],{"className":29843},[267],[60,29845],{"className":29846,"style":470},[469],[60,29848,448],{"className":29849},[474],[60,29851],{"className":29852,"style":470},[469],[60,29854,29856,29859,29862,29930,29933,29936,29939],{"className":29855},[118],[60,29857],{"className":29858,"style":12028},[122],[60,29860,817],{"className":29861},[127],[60,29863,29865,29868,29927],{"className":29864},[127],[60,29866],{"className":29867},[131,132],[60,29869,29871],{"className":29870},[79],[60,29872,29874,29919],{"className":29873},[139,140],[60,29875,29877,29916],{"className":29876},[144],[60,29878,29880,29894,29902],{"className":29879,"style":11547},[148],[60,29881,29882,29885],{"style":152},[60,29883],{"className":29884,"style":157},[156],[60,29886,29888],{"className":29887},[161,162,163,164],[60,29889,29891],{"className":29890},[127,164],[60,29892,23145],{"className":29893},[127,164],[60,29895,29896,29899],{"style":225},[60,29897],{"className":29898,"style":157},[156],[60,29900],{"className":29901,"style":233},[232],[60,29903,29904,29907],{"style":1105},[60,29905],{"className":29906,"style":157},[156],[60,29908,29910],{"className":29909},[161,162,163,164],[60,29911,29913],{"className":29912},[127,164],[60,29914,820],{"className":29915},[127,164],[60,29917,213],{"className":29918},[212],[60,29920,29922],{"className":29921},[144],[60,29923,29925],{"className":29924,"style":3907},[148],[60,29926],{},[60,29928],{"className":29929},[267,132],[60,29931,2152],{"className":29932},[127,178],[60,29934],{"className":29935,"style":924},[469],[60,29937,990],{"className":29938},[928],[60,29940],{"className":29941,"style":924},[469],[60,29943,29945,29948,30016,30019,30022,30025,30028,30031],{"className":29944},[118],[60,29946],{"className":29947,"style":12028},[122],[60,29949,29951,29954,30013],{"className":29950},[127],[60,29952],{"className":29953},[131,132],[60,29955,29957],{"className":29956},[79],[60,29958,29960,30005],{"className":29959},[139,140],[60,29961,29963,30002],{"className":29962},[144],[60,29964,29966,29980,29988],{"className":29965,"style":11547},[148],[60,29967,29968,29971],{"style":152},[60,29969],{"className":29970,"style":157},[156],[60,29972,29974],{"className":29973},[161,162,163,164],[60,29975,29977],{"className":29976},[127,164],[60,29978,23145],{"className":29979},[127,164],[60,29981,29982,29985],{"style":225},[60,29983],{"className":29984,"style":157},[156],[60,29986],{"className":29987,"style":233},[232],[60,29989,29990,29993],{"style":1105},[60,29991],{"className":29992,"style":157},[156],[60,29994,29996],{"className":29995},[161,162,163,164],[60,29997,29999],{"className":29998},[127,164],[60,30000,820],{"className":30001},[127,164],[60,30003,213],{"className":30004},[212],[60,30006,30008],{"className":30007},[144],[60,30009,30011],{"className":30010,"style":3907},[148],[60,30012],{},[60,30014],{"className":30015},[267,132],[60,30017,2152],{"className":30018},[127,178],[60,30020],{"className":30021,"style":653},[469],[60,30023,11088],{"className":30024},[1495],[60,30026],{"className":30027,"style":653},[469],[60,30029,23145],{"className":30030},[127],[60,30032,2152],{"className":30033},[127,178],[23,30035,30036,30039],{},[26,30037,30038],{},"Step 4: 积分（略去繁琐步骤，你需要自己练习分部积分）","\n这里积出来会比较长，但逻辑就是简单的积分。",[15,30041],{},[496,30043,30045,30046,19999,30316],{"id":30044},"_5-t2xtxx6t34t2t2-x-tx-x-6t-34t2t2xtxx6t34t2已知-x1tx2tlntx_1-t-x_2-tln-tx1tx2tlnt","(5) ",[60,30047,30049,30109],{"className":30048},[63],[60,30050,30052],{"className":30051},[67],[69,30053,30054],{"xmlns":71},[73,30055,30056,30106],{},[76,30057,30058,30064,30074,30076,30078,30084,30086,30088,30090,30093,30095,30097,30100],{},[550,30059,30060,30062],{},[84,30061,2152],{},[102,30063,814],{},[550,30065,30066,30068],{},[84,30067,359],{},[76,30069,30070,30072],{},[397,30071,557],{"mathvariant":86},[397,30073,557],{"mathvariant":86},[397,30075,817],{},[84,30077,2152],{},[550,30079,30080,30082],{},[84,30081,359],{},[397,30083,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,30085,990],{},[84,30087,359],{},[397,30089,448],{},[102,30091,30092],{},"6",[84,30094,2152],{},[397,30096,990],{},[102,30098,30099],{},"34",[550,30101,30102,30104],{},[84,30103,2152],{},[102,30105,814],{},[106,30107,30108],{"encoding":108},"t^2 x'' - tx' + x = 6t + 34t^2",[60,30110,30112,30189,30239,30257,30278],{"className":30111,"ariaHidden":114},[113],[60,30113,30115,30119,30148,30180,30183,30186],{"className":30114},[118],[60,30116],{"className":30117,"style":30118},[122],"height:0.8974em;vertical-align:-0.0833em;",[60,30120,30122,30125],{"className":30121},[127],[60,30123,2152],{"className":30124},[127,178],[60,30126,30128],{"className":30127},[183],[60,30129,30131],{"className":30130},[139],[60,30132,30134],{"className":30133},[144],[60,30135,30137],{"className":30136,"style":909},[148],[60,30138,30139,30142],{"style":608},[60,30140],{"className":30141,"style":325},[156],[60,30143,30145],{"className":30144},[161,162,163,164],[60,30146,814],{"className":30147},[127,164],[60,30149,30151,30154],{"className":30150},[127],[60,30152,359],{"className":30153},[127,178],[60,30155,30157],{"className":30156},[183],[60,30158,30160],{"className":30159},[139],[60,30161,30163],{"className":30162},[144],[60,30164,30166],{"className":30165,"style":605},[148],[60,30167,30168,30171],{"style":608},[60,30169],{"className":30170,"style":325},[156],[60,30172,30174],{"className":30173},[161,162,163,164],[60,30175,30177],{"className":30176},[127,164],[60,30178,17727],{"className":30179},[127,164],[60,30181],{"className":30182,"style":924},[469],[60,30184,817],{"className":30185},[928],[60,30187],{"className":30188,"style":924},[469],[60,30190,30192,30195,30198,30230,30233,30236],{"className":30191},[118],[60,30193],{"className":30194,"style":19924},[122],[60,30196,2152],{"className":30197},[127,178],[60,30199,30201,30204],{"className":30200},[127],[60,30202,359],{"className":30203},[127,178],[60,30205,30207],{"className":30206},[183],[60,30208,30210],{"className":30209},[139],[60,30211,30213],{"className":30212},[144],[60,30214,30216],{"className":30215,"style":605},[148],[60,30217,30218,30221],{"style":608},[60,30219],{"className":30220,"style":325},[156],[60,30222,30224],{"className":30223},[161,162,163,164],[60,30225,30227],{"className":30226},[127,164],[60,30228,557],{"className":30229},[127,164],[60,30231],{"className":30232,"style":924},[469],[60,30234,990],{"className":30235},[928],[60,30237],{"className":30238,"style":924},[469],[60,30240,30242,30245,30248,30251,30254],{"className":30241},[118],[60,30243],{"className":30244,"style":371},[122],[60,30246,359],{"className":30247},[127,178],[60,30249],{"className":30250,"style":470},[469],[60,30252,448],{"className":30253},[474],[60,30255],{"className":30256,"style":470},[469],[60,30258,30260,30263,30266,30269,30272,30275],{"className":30259},[118],[60,30261],{"className":30262,"style":1197},[122],[60,30264,30092],{"className":30265},[127],[60,30267,2152],{"className":30268},[127,178],[60,30270],{"className":30271,"style":924},[469],[60,30273,990],{"className":30274},[928],[60,30276],{"className":30277,"style":924},[469],[60,30279,30281,30284,30287],{"className":30280},[118],[60,30282],{"className":30283,"style":909},[122],[60,30285,30099],{"className":30286},[127],[60,30288,30290,30293],{"className":30289},[127],[60,30291,2152],{"className":30292},[127,178],[60,30294,30296],{"className":30295},[183],[60,30297,30299],{"className":30298},[139],[60,30300,30302],{"className":30301},[144],[60,30303,30305],{"className":30304,"style":909},[148],[60,30306,30307,30310],{"style":608},[60,30308],{"className":30309,"style":325},[156],[60,30311,30313],{"className":30312},[161,162,163,164],[60,30314,814],{"className":30315},[127,164],[60,30317,30319,30359],{"className":30318},[63],[60,30320,30322],{"className":30321},[67],[69,30323,30324],{"xmlns":71},[73,30325,30326,30356],{},[76,30327,30328,30334,30336,30338,30340,30346,30348,30350,30352,30354],{},[96,30329,30330,30332],{},[84,30331,359],{},[102,30333,820],{},[397,30335,448],{},[84,30337,2152],{},[397,30339,569],{"separator":114},[96,30341,30342,30344],{},[84,30343,359],{},[102,30345,814],{},[397,30347,448],{},[84,30349,2152],{},[84,30351,1462],{},[397,30353,1465],{},[84,30355,2152],{},[106,30357,30358],{"encoding":108},"x_1 = t, x_2 = t\\ln t",[60,30360,30362,30417,30482],{"className":30361,"ariaHidden":114},[113],[60,30363,30365,30368,30408,30411,30414],{"className":30364},[118],[60,30366],{"className":30367,"style":2734},[122],[60,30369,30371,30374],{"className":30370},[127],[60,30372,359],{"className":30373},[127,178],[60,30375,30377],{"className":30376},[183],[60,30378,30380,30400],{"className":30379},[139,140],[60,30381,30383,30397],{"className":30382},[144],[60,30384,30386],{"className":30385,"style":318},[148],[60,30387,30388,30391],{"style":1940},[60,30389],{"className":30390,"style":325},[156],[60,30392,30394],{"className":30393},[161,162,163,164],[60,30395,820],{"className":30396},[127,164],[60,30398,213],{"className":30399},[212],[60,30401,30403],{"className":30402},[144],[60,30404,30406],{"className":30405,"style":341},[148],[60,30407],{},[60,30409],{"className":30410,"style":470},[469],[60,30412,448],{"className":30413},[474],[60,30415],{"className":30416,"style":470},[469],[60,30418,30420,30424,30427,30430,30433,30473,30476,30479],{"className":30419},[118],[60,30421],{"className":30422,"style":30423},[122],"height:0.8095em;vertical-align:-0.1944em;",[60,30425,2152],{"className":30426},[127,178],[60,30428,569],{"className":30429},[649],[60,30431],{"className":30432,"style":653},[469],[60,30434,30436,30439],{"className":30435},[127],[60,30437,359],{"className":30438},[127,178],[60,30440,30442],{"className":30441},[183],[60,30443,30445,30465],{"className":30444},[139,140],[60,30446,30448,30462],{"className":30447},[144],[60,30449,30451],{"className":30450,"style":318},[148],[60,30452,30453,30456],{"style":1940},[60,30454],{"className":30455,"style":325},[156],[60,30457,30459],{"className":30458},[161,162,163,164],[60,30460,814],{"className":30461},[127,164],[60,30463,213],{"className":30464},[212],[60,30466,30468],{"className":30467},[144],[60,30469,30471],{"className":30470,"style":341},[148],[60,30472],{},[60,30474],{"className":30475,"style":470},[469],[60,30477,448],{"className":30478},[474],[60,30480],{"className":30481,"style":470},[469],[60,30483,30485,30488,30491,30494,30497,30500],{"className":30484},[118],[60,30486],{"className":30487,"style":13418},[122],[60,30489,2152],{"className":30490},[127,178],[60,30492],{"className":30493,"style":653},[469],[60,30495,1462],{"className":30496},[1495],[60,30498],{"className":30499,"style":653},[469],[60,30501,2152],{"className":30502},[127,178],[23,30504,30505,30508,30573,30574,17518,30633,30694,30695,31129,31130,31289,31290,31381],{},[26,30506,30507],{},"Step 1: 检查系数（陷阱！！）",[60,30509,30511,30532],{"className":30510},[63],[60,30512,30514],{"className":30513},[67],[69,30515,30516],{"xmlns":71},[73,30517,30518,30530],{},[76,30519,30520],{},[550,30521,30522,30524],{},[84,30523,359],{},[76,30525,30526,30528],{},[397,30527,557],{"mathvariant":86},[397,30529,557],{"mathvariant":86},[106,30531,20269],{"encoding":108},[60,30533,30535],{"className":30534,"ariaHidden":114},[113],[60,30536,30538,30541],{"className":30537},[118],[60,30539],{"className":30540,"style":605},[122],[60,30542,30544,30547],{"className":30543},[127],[60,30545,359],{"className":30546},[127,178],[60,30548,30550],{"className":30549},[183],[60,30551,30553],{"className":30552},[139],[60,30554,30556],{"className":30555},[144],[60,30557,30559],{"className":30558,"style":605},[148],[60,30560,30561,30564],{"style":608},[60,30562],{"className":30563,"style":325},[156],[60,30565,30567],{"className":30566},[161,162,163,164],[60,30568,30570],{"className":30569},[127,164],[60,30571,17727],{"className":30572},[127,164]," 前面是 ",[60,30575,30577,30595],{"className":30576},[63],[60,30578,30580],{"className":30579},[67],[69,30581,30582],{"xmlns":71},[73,30583,30584,30592],{},[76,30585,30586],{},[550,30587,30588,30590],{},[84,30589,2152],{},[102,30591,814],{},[106,30593,30594],{"encoding":108},"t^2",[60,30596,30598],{"className":30597,"ariaHidden":114},[113],[60,30599,30601,30604],{"className":30600},[118],[60,30602],{"className":30603,"style":909},[122],[60,30605,30607,30610],{"className":30606},[127],[60,30608,2152],{"className":30609},[127,178],[60,30611,30613],{"className":30612},[183],[60,30614,30616],{"className":30615},[139],[60,30617,30619],{"className":30618},[144],[60,30620,30622],{"className":30621,"style":909},[148],[60,30623,30624,30627],{"style":608},[60,30625],{"className":30626,"style":325},[156],[60,30628,30630],{"className":30629},[161,162,163,164],[60,30631,814],{"className":30632},[127,164],[26,30634,30635,30636],{},"必须两边同时除以 ",[60,30637,30639,30656],{"className":30638},[63],[60,30640,30642],{"className":30641},[67],[69,30643,30644],{"xmlns":71},[73,30645,30646,30654],{},[76,30647,30648],{},[550,30649,30650,30652],{},[84,30651,2152],{},[102,30653,814],{},[106,30655,30594],{"encoding":108},[60,30657,30659],{"className":30658,"ariaHidden":114},[113],[60,30660,30662,30665],{"className":30661},[118],[60,30663],{"className":30664,"style":909},[122],[60,30666,30668,30671],{"className":30667},[127],[60,30669,2152],{"className":30670},[127,178],[60,30672,30674],{"className":30673},[183],[60,30675,30677],{"className":30676},[139],[60,30678,30680],{"className":30679},[144],[60,30681,30683],{"className":30682,"style":909},[148],[60,30684,30685,30688],{"style":608},[60,30686],{"className":30687,"style":325},[156],[60,30689,30691],{"className":30690},[161,162,163,164],[60,30692,814],{"className":30693},[127,164],"！\n标准化方程：\n",[60,30696,30698,30760],{"className":30697},[63],[60,30699,30701],{"className":30700},[67],[69,30702,30703],{"xmlns":71},[73,30704,30705,30757],{},[76,30706,30707,30717,30719,30725,30731,30733,30743,30745,30747,30753,30755],{},[550,30708,30709,30711],{},[84,30710,359],{},[76,30712,30713,30715],{},[397,30714,557],{"mathvariant":86},[397,30716,557],{"mathvariant":86},[397,30718,817],{},[79,30720,30721,30723],{},[102,30722,820],{},[84,30724,2152],{},[550,30726,30727,30729],{},[84,30728,359],{},[397,30730,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,30732,990],{},[79,30734,30735,30737],{},[102,30736,820],{},[550,30738,30739,30741],{},[84,30740,2152],{},[102,30742,814],{},[84,30744,359],{},[397,30746,448],{},[79,30748,30749,30751],{},[102,30750,30092],{},[84,30752,2152],{},[397,30754,990],{},[102,30756,30099],{},[106,30758,30759],{"encoding":108},"x'' - \\frac{1}{t}x' + \\frac{1}{t^2}x = \\frac{6}{t} + 34",[60,30761,30763,30810,30925,31037,31120],{"className":30762,"ariaHidden":114},[113],[60,30764,30766,30769,30801,30804,30807],{"className":30765},[118],[60,30767],{"className":30768,"style":19924},[122],[60,30770,30772,30775],{"className":30771},[127],[60,30773,359],{"className":30774},[127,178],[60,30776,30778],{"className":30777},[183],[60,30779,30781],{"className":30780},[139],[60,30782,30784],{"className":30783},[144],[60,30785,30787],{"className":30786,"style":605},[148],[60,30788,30789,30792],{"style":608},[60,30790],{"className":30791,"style":325},[156],[60,30793,30795],{"className":30794},[161,162,163,164],[60,30796,30798],{"className":30797},[127,164],[60,30799,17727],{"className":30800},[127,164],[60,30802],{"className":30803,"style":924},[469],[60,30805,817],{"className":30806},[928],[60,30808],{"className":30809,"style":924},[469],[60,30811,30813,30816,30884,30916,30919,30922],{"className":30812},[118],[60,30814],{"className":30815,"style":12028},[122],[60,30817,30819,30822,30881],{"className":30818},[127],[60,30820],{"className":30821},[131,132],[60,30823,30825],{"className":30824},[79],[60,30826,30828,30873],{"className":30827},[139,140],[60,30829,30831,30870],{"className":30830},[144],[60,30832,30834,30848,30856],{"className":30833,"style":11547},[148],[60,30835,30836,30839],{"style":152},[60,30837],{"className":30838,"style":157},[156],[60,30840,30842],{"className":30841},[161,162,163,164],[60,30843,30845],{"className":30844},[127,164],[60,30846,2152],{"className":30847},[127,178,164],[60,30849,30850,30853],{"style":225},[60,30851],{"className":30852,"style":157},[156],[60,30854],{"className":30855,"style":233},[232],[60,30857,30858,30861],{"style":1105},[60,30859],{"className":30860,"style":157},[156],[60,30862,30864],{"className":30863},[161,162,163,164],[60,30865,30867],{"className":30866},[127,164],[60,30868,820],{"className":30869},[127,164],[60,30871,213],{"className":30872},[212],[60,30874,30876],{"className":30875},[144],[60,30877,30879],{"className":30878,"style":3907},[148],[60,30880],{},[60,30882],{"className":30883},[267,132],[60,30885,30887,30890],{"className":30886},[127],[60,30888,359],{"className":30889},[127,178],[60,30891,30893],{"className":30892},[183],[60,30894,30896],{"className":30895},[139],[60,30897,30899],{"className":30898},[144],[60,30900,30902],{"className":30901,"style":605},[148],[60,30903,30904,30907],{"style":608},[60,30905],{"className":30906,"style":325},[156],[60,30908,30910],{"className":30909},[161,162,163,164],[60,30911,30913],{"className":30912},[127,164],[60,30914,557],{"className":30915},[127,164],[60,30917],{"className":30918,"style":924},[469],[60,30920,990],{"className":30921},[928],[60,30923],{"className":30924,"style":924},[469],[60,30926,30928,30931,31025,31028,31031,31034],{"className":30927},[118],[60,30929],{"className":30930,"style":12028},[122],[60,30932,30934,30937,31022],{"className":30933},[127],[60,30935],{"className":30936},[131,132],[60,30938,30940],{"className":30939},[79],[60,30941,30943,31014],{"className":30942},[139,140],[60,30944,30946,31011],{"className":30945},[144],[60,30947,30949,30989,30997],{"className":30948,"style":11547},[148],[60,30950,30951,30954],{"style":152},[60,30952],{"className":30953,"style":157},[156],[60,30955,30957],{"className":30956},[161,162,163,164],[60,30958,30960],{"className":30959},[127,164],[60,30961,30963,30966],{"className":30962},[127,164],[60,30964,2152],{"className":30965},[127,178,164],[60,30967,30969],{"className":30968},[183],[60,30970,30972],{"className":30971},[139],[60,30973,30975],{"className":30974},[144],[60,30976,30978],{"className":30977,"style":16988},[148],[60,30979,30980,30983],{"style":1085},[60,30981],{"className":30982,"style":200},[156],[60,30984,30986],{"className":30985},[161,204,205,164],[60,30987,814],{"className":30988},[127,164],[60,30990,30991,30994],{"style":225},[60,30992],{"className":30993,"style":157},[156],[60,30995],{"className":30996,"style":233},[232],[60,30998,30999,31002],{"style":1105},[60,31000],{"className":31001,"style":157},[156],[60,31003,31005],{"className":31004},[161,162,163,164],[60,31006,31008],{"className":31007},[127,164],[60,31009,820],{"className":31010},[127,164],[60,31012,213],{"className":31013},[212],[60,31015,31017],{"className":31016},[144],[60,31018,31020],{"className":31019,"style":3907},[148],[60,31021],{},[60,31023],{"className":31024},[267,132],[60,31026,359],{"className":31027},[127,178],[60,31029],{"className":31030,"style":470},[469],[60,31032,448],{"className":31033},[474],[60,31035],{"className":31036,"style":470},[469],[60,31038,31040,31043,31111,31114,31117],{"className":31039},[118],[60,31041],{"className":31042,"style":12028},[122],[60,31044,31046,31049,31108],{"className":31045},[127],[60,31047],{"className":31048},[131,132],[60,31050,31052],{"className":31051},[79],[60,31053,31055,31100],{"className":31054},[139,140],[60,31056,31058,31097],{"className":31057},[144],[60,31059,31061,31075,31083],{"className":31060,"style":11547},[148],[60,31062,31063,31066],{"style":152},[60,31064],{"className":31065,"style":157},[156],[60,31067,31069],{"className":31068},[161,162,163,164],[60,31070,31072],{"className":31071},[127,164],[60,31073,2152],{"className":31074},[127,178,164],[60,31076,31077,31080],{"style":225},[60,31078],{"className":31079,"style":157},[156],[60,31081],{"className":31082,"style":233},[232],[60,31084,31085,31088],{"style":1105},[60,31086],{"className":31087,"style":157},[156],[60,31089,31091],{"className":31090},[161,162,163,164],[60,31092,31094],{"className":31093},[127,164],[60,31095,30092],{"className":31096},[127,164],[60,31098,213],{"className":31099},[212],[60,31101,31103],{"className":31102},[144],[60,31104,31106],{"className":31105,"style":3907},[148],[60,31107],{},[60,31109],{"className":31110},[267,132],[60,31112],{"className":31113,"style":924},[469],[60,31115,990],{"className":31116},[928],[60,31118],{"className":31119,"style":924},[469],[60,31121,31123,31126],{"className":31122},[118],[60,31124],{"className":31125,"style":484},[122],[60,31127,30099],{"className":31128},[127],"\n所以，",[26,31131,31132],{},[60,31133,31135,31167],{"className":31134},[63],[60,31136,31138],{"className":31137},[67],[69,31139,31140],{"xmlns":71},[73,31141,31142,31164],{},[76,31143,31144,31146,31148,31150,31152,31154,31160,31162],{},[84,31145,562],{},[397,31147,400],{"stretchy":399},[84,31149,2152],{},[397,31151,405],{"stretchy":399},[397,31153,448],{},[79,31155,31156,31158],{},[102,31157,30092],{},[84,31159,2152],{},[397,31161,990],{},[102,31163,30099],{},[106,31165,31166],{"encoding":108},"f(t) = \\frac{6}{t} + 34",[60,31168,31170,31197,31280],{"className":31169,"ariaHidden":114},[113],[60,31171,31173,31176,31179,31182,31185,31188,31191,31194],{"className":31172},[118],[60,31174],{"className":31175,"style":418},[122],[60,31177,562],{"className":31178,"style":639},[127,178],[60,31180,400],{"className":31181},[131],[60,31183,2152],{"className":31184},[127,178],[60,31186,405],{"className":31187},[267],[60,31189],{"className":31190,"style":470},[469],[60,31192,448],{"className":31193},[474],[60,31195],{"className":31196,"style":470},[469],[60,31198,31200,31203,31271,31274,31277],{"className":31199},[118],[60,31201],{"className":31202,"style":12028},[122],[60,31204,31206,31209,31268],{"className":31205},[127],[60,31207],{"className":31208},[131,132],[60,31210,31212],{"className":31211},[79],[60,31213,31215,31260],{"className":31214},[139,140],[60,31216,31218,31257],{"className":31217},[144],[60,31219,31221,31235,31243],{"className":31220,"style":11547},[148],[60,31222,31223,31226],{"style":152},[60,31224],{"className":31225,"style":157},[156],[60,31227,31229],{"className":31228},[161,162,163,164],[60,31230,31232],{"className":31231},[127,164],[60,31233,2152],{"className":31234},[127,178,164],[60,31236,31237,31240],{"style":225},[60,31238],{"className":31239,"style":157},[156],[60,31241],{"className":31242,"style":233},[232],[60,31244,31245,31248],{"style":1105},[60,31246],{"className":31247,"style":157},[156],[60,31249,31251],{"className":31250},[161,162,163,164],[60,31252,31254],{"className":31253},[127,164],[60,31255,30092],{"className":31256},[127,164],[60,31258,213],{"className":31259},[212],[60,31261,31263],{"className":31262},[144],[60,31264,31266],{"className":31265,"style":3907},[148],[60,31267],{},[60,31269],{"className":31270},[267,132],[60,31272],{"className":31273,"style":924},[469],[60,31275,990],{"className":31276},[928],[60,31278],{"className":31279,"style":924},[469],[60,31281,31283,31286],{"className":31282},[118],[60,31284],{"className":31285,"style":484},[122],[60,31287,30099],{"className":31288},[127],"。如果你用 ",[60,31291,31293,31319],{"className":31292},[63],[60,31294,31296],{"className":31295},[67],[69,31297,31298],{"xmlns":71},[73,31299,31300,31316],{},[76,31301,31302,31304,31306,31308,31310],{},[102,31303,30092],{},[84,31305,2152],{},[397,31307,990],{},[102,31309,30099],{},[550,31311,31312,31314],{},[84,31313,2152],{},[102,31315,814],{},[106,31317,31318],{"encoding":108},"6t+34t^2",[60,31320,31322,31343],{"className":31321,"ariaHidden":114},[113],[60,31323,31325,31328,31331,31334,31337,31340],{"className":31324},[118],[60,31326],{"className":31327,"style":1197},[122],[60,31329,30092],{"className":31330},[127],[60,31332,2152],{"className":31333},[127,178],[60,31335],{"className":31336,"style":924},[469],[60,31338,990],{"className":31339},[928],[60,31341],{"className":31342,"style":924},[469],[60,31344,31346,31349,31352],{"className":31345},[118],[60,31347],{"className":31348,"style":909},[122],[60,31350,30099],{"className":31351},[127],[60,31353,31355,31358],{"className":31354},[127],[60,31356,2152],{"className":31357},[127,178],[60,31359,31361],{"className":31360},[183],[60,31362,31364],{"className":31363},[139],[60,31365,31367],{"className":31366},[144],[60,31368,31370],{"className":31369,"style":909},[148],[60,31371,31372,31375],{"style":608},[60,31373],{"className":31374,"style":325},[156],[60,31376,31378],{"className":31377},[161,162,163,164],[60,31379,814],{"className":31380},[127,164]," 算，就全错了。",[23,31383,31384,31386,31589],{},[26,31385,26975],{},[60,31387,31389,31429],{"className":31388},[63],[60,31390,31392],{"className":31391},[67],[69,31393,31394],{"xmlns":71},[73,31395,31396,31426],{},[76,31397,31398,31404,31406,31408,31410,31412,31414,31422,31424],{},[96,31399,31400,31402],{},[84,31401,359],{},[102,31403,820],{},[397,31405,448],{},[84,31407,2152],{},[13095,31409,18294],{},[397,31411,18297],{},[13095,31413,18294],{},[2127,31415,31416,31418,31420],{},[84,31417,359],{},[102,31419,820],{},[397,31421,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,31423,448],{},[102,31425,820],{},[106,31427,31428],{"encoding":108},"x_1 = t \\implies x_1' = 1",[60,31430,31432,31487,31511,31580],{"className":31431,"ariaHidden":114},[113],[60,31433,31435,31438,31478,31481,31484],{"className":31434},[118],[60,31436],{"className":31437,"style":2734},[122],[60,31439,31441,31444],{"className":31440},[127],[60,31442,359],{"className":31443},[127,178],[60,31445,31447],{"className":31446},[183],[60,31448,31450,31470],{"className":31449},[139,140],[60,31451,31453,31467],{"className":31452},[144],[60,31454,31456],{"className":31455,"style":318},[148],[60,31457,31458,31461],{"style":1940},[60,31459],{"className":31460,"style":325},[156],[60,31462,31464],{"className":31463},[161,162,163,164],[60,31465,820],{"className":31466},[127,164],[60,31468,213],{"className":31469},[212],[60,31471,31473],{"className":31472},[144],[60,31474,31476],{"className":31475,"style":341},[148],[60,31477],{},[60,31479],{"className":31480,"style":470},[469],[60,31482,448],{"className":31483},[474],[60,31485],{"className":31486,"style":470},[469],[60,31488,31490,31493,31496,31499,31502,31505,31508],{"className":31489},[118],[60,31491],{"className":31492,"style":22029},[122],[60,31494,2152],{"className":31495},[127,178],[60,31497],{"className":31498,"style":470},[469],[60,31500],{"className":31501,"style":470},[469],[60,31503,18297],{"className":31504},[474],[60,31506],{"className":31507,"style":470},[469],[60,31509],{"className":31510,"style":470},[469],[60,31512,31514,31517,31571,31574,31577],{"className":31513},[118],[60,31515],{"className":31516,"style":17392},[122],[60,31518,31520,31523],{"className":31519},[127],[60,31521,359],{"className":31522},[127,178],[60,31524,31526],{"className":31525},[183],[60,31527,31529,31563],{"className":31528},[139,140],[60,31530,31532,31560],{"className":31531},[144],[60,31533,31535,31546],{"className":31534,"style":605},[148],[60,31536,31537,31540],{"style":17413},[60,31538],{"className":31539,"style":325},[156],[60,31541,31543],{"className":31542},[161,162,163,164],[60,31544,820],{"className":31545},[127,164],[60,31547,31548,31551],{"style":608},[60,31549],{"className":31550,"style":325},[156],[60,31552,31554],{"className":31553},[161,162,163,164],[60,31555,31557],{"className":31556},[127,164],[60,31558,557],{"className":31559},[127,164],[60,31561,213],{"className":31562},[212],[60,31564,31566],{"className":31565},[144],[60,31567,31569],{"className":31568,"style":17446},[148],[60,31570],{},[60,31572],{"className":31573,"style":470},[469],[60,31575,448],{"className":31576},[474],[60,31578],{"className":31579,"style":470},[469],[60,31581,31583,31586],{"className":31582},[118],[60,31584],{"className":31585,"style":484},[122],[60,31587,820],{"className":31588},[127],[60,31590,31592,31646],{"className":31591},[63],[60,31593,31595],{"className":31594},[67],[69,31596,31597],{"xmlns":71},[73,31598,31599,31643],{},[76,31600,31601,31607,31609,31611,31613,31615,31617,31619,31621,31623,31631,31633,31635,31637,31639,31641],{},[96,31602,31603,31605],{},[84,31604,359],{},[102,31606,814],{},[397,31608,448],{},[84,31610,2152],{},[84,31612,1462],{},[397,31614,1465],{},[84,31616,2152],{},[13095,31618,18294],{},[397,31620,18297],{},[13095,31622,18294],{},[2127,31624,31625,31627,31629],{},[84,31626,359],{},[102,31628,814],{},[397,31630,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,31632,448],{},[84,31634,1462],{},[397,31636,1465],{},[84,31638,2152],{},[397,31640,990],{},[102,31642,820],{},[106,31644,31645],{"encoding":108},"x_2 = t\\ln t \\implies x_2' = \\ln t + 1",[60,31647,31649,31704,31741,31810,31835],{"className":31648,"ariaHidden":114},[113],[60,31650,31652,31655,31695,31698,31701],{"className":31651},[118],[60,31653],{"className":31654,"style":2734},[122],[60,31656,31658,31661],{"className":31657},[127],[60,31659,359],{"className":31660},[127,178],[60,31662,31664],{"className":31663},[183],[60,31665,31667,31687],{"className":31666},[139,140],[60,31668,31670,31684],{"className":31669},[144],[60,31671,31673],{"className":31672,"style":318},[148],[60,31674,31675,31678],{"style":1940},[60,31676],{"className":31677,"style":325},[156],[60,31679,31681],{"className":31680},[161,162,163,164],[60,31682,814],{"className":31683},[127,164],[60,31685,213],{"className":31686},[212],[60,31688,31690],{"className":31689},[144],[60,31691,31693],{"className":31692,"style":341},[148],[60,31694],{},[60,31696],{"className":31697,"style":470},[469],[60,31699,448],{"className":31700},[474],[60,31702],{"className":31703,"style":470},[469],[60,31705,31707,31711,31714,31717,31720,31723,31726,31729,31732,31735,31738],{"className":31706},[118],[60,31708],{"className":31709,"style":31710},[122],"height:0.7184em;vertical-align:-0.024em;",[60,31712,2152],{"className":31713},[127,178],[60,31715],{"className":31716,"style":653},[469],[60,31718,1462],{"className":31719},[1495],[60,31721],{"className":31722,"style":653},[469],[60,31724,2152],{"className":31725},[127,178],[60,31727],{"className":31728,"style":470},[469],[60,31730],{"className":31731,"style":470},[469],[60,31733,18297],{"className":31734},[474],[60,31736],{"className":31737,"style":470},[469],[60,31739],{"className":31740,"style":470},[469],[60,31742,31744,31747,31801,31804,31807],{"className":31743},[118],[60,31745],{"className":31746,"style":17392},[122],[60,31748,31750,31753],{"className":31749},[127],[60,31751,359],{"className":31752},[127,178],[60,31754,31756],{"className":31755},[183],[60,31757,31759,31793],{"className":31758},[139,140],[60,31760,31762,31790],{"className":31761},[144],[60,31763,31765,31776],{"className":31764,"style":605},[148],[60,31766,31767,31770],{"style":17413},[60,31768],{"className":31769,"style":325},[156],[60,31771,31773],{"className":31772},[161,162,163,164],[60,31774,814],{"className":31775},[127,164],[60,31777,31778,31781],{"style":608},[60,31779],{"className":31780,"style":325},[156],[60,31782,31784],{"className":31783},[161,162,163,164],[60,31785,31787],{"className":31786},[127,164],[60,31788,557],{"className":31789},[127,164],[60,31791,213],{"className":31792},[212],[60,31794,31796],{"className":31795},[144],[60,31797,31799],{"className":31798,"style":17446},[148],[60,31800],{},[60,31802],{"className":31803,"style":470},[469],[60,31805,448],{"className":31806},[474],[60,31808],{"className":31809,"style":470},[469],[60,31811,31813,31817,31820,31823,31826,31829,31832],{"className":31812},[118],[60,31814],{"className":31815,"style":31816},[122],"height:0.7778em;vertical-align:-0.0833em;",[60,31818,1462],{"className":31819},[1495],[60,31821],{"className":31822,"style":653},[469],[60,31824,2152],{"className":31825},[127,178],[60,31827],{"className":31828,"style":924},[469],[60,31830,990],{"className":31831},[928],[60,31833],{"className":31834,"style":924},[469],[60,31836,31838,31841],{"className":31837},[118],[60,31839],{"className":31840,"style":484},[122],[60,31842,820],{"className":31843},[127],[23,31845,31846,31847,21834],{},"[\n",[60,31848,31850,31964],{"className":31849},[63],[60,31851,31853],{"className":31852},[67],[69,31854,31855],{"xmlns":71},[73,31856,31857,31961],{},[76,31858,31859,31861],{},[397,31860,20568],{"fence":114},[20570,31862,31863,31903],{"rowspacing":20572,"columnalign":20573,"columnspacing":13091},[20575,31864,31865],{},[20578,31866,31867],{},[20581,31868,31869],{"scriptlevel":104,"displaystyle":399},[76,31870,31871,31879,31881,31883,31891,31893,31895,31897,31899,31901],{},[2127,31872,31873,31875,31877],{},[84,31874,20410],{},[102,31876,820],{},[397,31878,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,31880,2152],{},[397,31882,990],{},[2127,31884,31885,31887,31889],{},[84,31886,20410],{},[102,31888,814],{},[397,31890,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,31892,2152],{},[84,31894,1462],{},[397,31896,1465],{},[84,31898,2152],{},[397,31900,448],{},[102,31902,104],{},[20575,31904,31905],{},[20578,31906,31907],{},[20581,31908,31909],{"scriptlevel":104,"displaystyle":399},[76,31910,31911,31919,31921,31923,31925,31927,31935,31937,31939,31941,31943,31945,31947,31949,31951,31957,31959],{},[2127,31912,31913,31915,31917],{},[84,31914,20410],{},[102,31916,820],{},[397,31918,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,31920,400],{"stretchy":399},[102,31922,820],{},[397,31924,405],{"stretchy":399},[397,31926,990],{},[2127,31928,31929,31931,31933],{},[84,31930,20410],{},[102,31932,814],{},[397,31934,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,31936,400],{"stretchy":399},[84,31938,1462],{},[397,31940,1465],{},[84,31942,2152],{},[397,31944,990],{},[102,31946,820],{},[397,31948,405],{"stretchy":399},[397,31950,448],{},[79,31952,31953,31955],{},[102,31954,30092],{},[84,31956,2152],{},[397,31958,990],{},[102,31960,30099],{},[106,31962,31963],{"encoding":108},"\\begin{cases}\nc_1' t + c_2' t\\ln t = 0 \\\\\nc_1' (1) + c_2' (\\ln t + 1) = \\frac{6}{t} + 34\n\\end{cases}",[60,31965,31967],{"className":31966,"ariaHidden":114},[113],[60,31968,31970,31973],{"className":31969},[118],[60,31971],{"className":31972,"style":20819},[122],[60,31974,31976,31982,32416],{"className":31975},[2326],[60,31977,31979],{"className":31978,"style":2331},[131,2330],[60,31980,20568],{"className":31981},[2335,20829],[60,31983,31985],{"className":31984},[127],[60,31986,31988],{"className":31987},[20570],[60,31989,31991],{"className":31990},[20839],[60,31992,31994,32408],{"className":31993},[139,140],[60,31995,31997,32405],{"className":31996},[144],[60,31998,32000,32155],{"className":31999,"style":20849},[148],[60,32001,32002,32005],{"style":20852},[60,32003],{"className":32004,"style":20856},[156],[60,32006,32008,32062,32065,32068,32071,32074,32128,32131,32134,32137,32140,32143,32146,32149,32152],{"className":32007},[127],[60,32009,32011,32014],{"className":32010},[127],[60,32012,20410],{"className":32013},[127,178],[60,32015,32017],{"className":32016},[183],[60,32018,32020,32054],{"className":32019},[139,140],[60,32021,32023,32051],{"className":32022},[144],[60,32024,32026,32037],{"className":32025,"style":605},[148],[60,32027,32028,32031],{"style":17413},[60,32029],{"className":32030,"style":325},[156],[60,32032,32034],{"className":32033},[161,162,163,164],[60,32035,820],{"className":32036},[127,164],[60,32038,32039,32042],{"style":608},[60,32040],{"className":32041,"style":325},[156],[60,32043,32045],{"className":32044},[161,162,163,164],[60,32046,32048],{"className":32047},[127,164],[60,32049,557],{"className":32050},[127,164],[60,32052,213],{"className":32053},[212],[60,32055,32057],{"className":32056},[144],[60,32058,32060],{"className":32059,"style":17446},[148],[60,32061],{},[60,32063,2152],{"className":32064},[127,178],[60,32066],{"className":32067,"style":924},[469],[60,32069,990],{"className":32070},[928],[60,32072],{"className":32073,"style":924},[469],[60,32075,32077,32080],{"className":32076},[127],[60,32078,20410],{"className":32079},[127,178],[60,32081,32083],{"className":32082},[183],[60,32084,32086,32120],{"className":32085},[139,140],[60,32087,32089,32117],{"className":32088},[144],[60,32090,32092,32103],{"className":32091,"style":605},[148],[60,32093,32094,32097],{"style":17413},[60,32095],{"className":32096,"style":325},[156],[60,32098,32100],{"className":32099},[161,162,163,164],[60,32101,814],{"className":32102},[127,164],[60,32104,32105,32108],{"style":608},[60,32106],{"className":32107,"style":325},[156],[60,32109,32111],{"className":32110},[161,162,163,164],[60,32112,32114],{"className":32113},[127,164],[60,32115,557],{"className":32116},[127,164],[60,32118,213],{"className":32119},[212],[60,32121,32123],{"className":32122},[144],[60,32124,32126],{"className":32125,"style":17446},[148],[60,32127],{},[60,32129,2152],{"className":32130},[127,178],[60,32132],{"className":32133,"style":653},[469],[60,32135,1462],{"className":32136},[1495],[60,32138],{"className":32139,"style":653},[469],[60,32141,2152],{"className":32142},[127,178],[60,32144],{"className":32145,"style":470},[469],[60,32147,448],{"className":32148},[474],[60,32150],{"className":32151,"style":470},[469],[60,32153,104],{"className":32154},[127],[60,32156,32157,32160],{"style":21055},[60,32158],{"className":32159,"style":20856},[156],[60,32161,32163,32217,32220,32223,32226,32229,32232,32235,32289,32292,32295,32298,32301,32304,32307,32310,32313,32316,32319,32322,32325,32393,32396,32399,32402],{"className":32162},[127],[60,32164,32166,32169],{"className":32165},[127],[60,32167,20410],{"className":32168},[127,178],[60,32170,32172],{"className":32171},[183],[60,32173,32175,32209],{"className":32174},[139,140],[60,32176,32178,32206],{"className":32177},[144],[60,32179,32181,32192],{"className":32180,"style":605},[148],[60,32182,32183,32186],{"style":17413},[60,32184],{"className":32185,"style":325},[156],[60,32187,32189],{"className":32188},[161,162,163,164],[60,32190,820],{"className":32191},[127,164],[60,32193,32194,32197],{"style":608},[60,32195],{"className":32196,"style":325},[156],[60,32198,32200],{"className":32199},[161,162,163,164],[60,32201,32203],{"className":32202},[127,164],[60,32204,557],{"className":32205},[127,164],[60,32207,213],{"className":32208},[212],[60,32210,32212],{"className":32211},[144],[60,32213,32215],{"className":32214,"style":17446},[148],[60,32216],{},[60,32218,400],{"className":32219},[131],[60,32221,820],{"className":32222},[127],[60,32224,405],{"className":32225},[267],[60,32227],{"className":32228,"style":924},[469],[60,32230,990],{"className":32231},[928],[60,32233],{"className":32234,"style":924},[469],[60,32236,32238,32241],{"className":32237},[127],[60,32239,20410],{"className":32240},[127,178],[60,32242,32244],{"className":32243},[183],[60,32245,32247,32281],{"className":32246},[139,140],[60,32248,32250,32278],{"className":32249},[144],[60,32251,32253,32264],{"className":32252,"style":605},[148],[60,32254,32255,32258],{"style":17413},[60,32256],{"className":32257,"style":325},[156],[60,32259,32261],{"className":32260},[161,162,163,164],[60,32262,814],{"className":32263},[127,164],[60,32265,32266,32269],{"style":608},[60,32267],{"className":32268,"style":325},[156],[60,32270,32272],{"className":32271},[161,162,163,164],[60,32273,32275],{"className":32274},[127,164],[60,32276,557],{"className":32277},[127,164],[60,32279,213],{"className":32280},[212],[60,32282,32284],{"className":32283},[144],[60,32285,32287],{"className":32286,"style":17446},[148],[60,32288],{},[60,32290,400],{"className":32291},[131],[60,32293,1462],{"className":32294},[1495],[60,32296],{"className":32297,"style":653},[469],[60,32299,2152],{"className":32300},[127,178],[60,32302],{"className":32303,"style":924},[469],[60,32305,990],{"className":32306},[928],[60,32308],{"className":32309,"style":924},[469],[60,32311,820],{"className":32312},[127],[60,32314,405],{"className":32315},[267],[60,32317],{"className":32318,"style":470},[469],[60,32320,448],{"className":32321},[474],[60,32323],{"className":32324,"style":470},[469],[60,32326,32328,32331,32390],{"className":32327},[127],[60,32329],{"className":32330},[131,132],[60,32332,32334],{"className":32333},[79],[60,32335,32337,32382],{"className":32336},[139,140],[60,32338,32340,32379],{"className":32339},[144],[60,32341,32343,32357,32365],{"className":32342,"style":11547},[148],[60,32344,32345,32348],{"style":152},[60,32346],{"className":32347,"style":157},[156],[60,32349,32351],{"className":32350},[161,162,163,164],[60,32352,32354],{"className":32353},[127,164],[60,32355,2152],{"className":32356},[127,178,164],[60,32358,32359,32362],{"style":225},[60,32360],{"className":32361,"style":157},[156],[60,32363],{"className":32364,"style":233},[232],[60,32366,32367,32370],{"style":1105},[60,32368],{"className":32369,"style":157},[156],[60,32371,32373],{"className":32372},[161,162,163,164],[60,32374,32376],{"className":32375},[127,164],[60,32377,30092],{"className":32378},[127,164],[60,32380,213],{"className":32381},[212],[60,32383,32385],{"className":32384},[144],[60,32386,32388],{"className":32387,"style":3907},[148],[60,32389],{},[60,32391],{"className":32392},[267,132],[60,32394],{"className":32395,"style":924},[469],[60,32397,990],{"className":32398},[928],[60,32400],{"className":32401,"style":924},[469],[60,32403,30099],{"className":32404},[127],[60,32406,213],{"className":32407},[212],[60,32409,32411],{"className":32410},[144],[60,32412,32414],{"className":32413,"style":21340},[148],[60,32415],{},[60,32417],{"className":32418},[267,132],[23,32420,32421,32423,32424,32612,32613,33011],{},[26,32422,21839],{},"\n由第一式：",[60,32425,32427,32465],{"className":32426},[63],[60,32428,32430],{"className":32429},[67],[69,32431,32432],{"xmlns":71},[73,32433,32434,32462],{},[76,32435,32436,32444,32446,32448,32456,32458,32460],{},[2127,32437,32438,32440,32442],{},[84,32439,20410],{},[102,32441,820],{},[397,32443,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,32445,448],{},[397,32447,817],{},[2127,32449,32450,32452,32454],{},[84,32451,20410],{},[102,32453,814],{},[397,32455,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,32457,1462],{},[397,32459,1465],{},[84,32461,2152],{},[106,32463,32464],{"encoding":108},"c_1' = -c_2' \\ln t",[60,32466,32468,32537],{"className":32467,"ariaHidden":114},[113],[60,32469,32471,32474,32528,32531,32534],{"className":32470},[118],[60,32472],{"className":32473,"style":17392},[122],[60,32475,32477,32480],{"className":32476},[127],[60,32478,20410],{"className":32479},[127,178],[60,32481,32483],{"className":32482},[183],[60,32484,32486,32520],{"className":32485},[139,140],[60,32487,32489,32517],{"className":32488},[144],[60,32490,32492,32503],{"className":32491,"style":605},[148],[60,32493,32494,32497],{"style":17413},[60,32495],{"className":32496,"style":325},[156],[60,32498,32500],{"className":32499},[161,162,163,164],[60,32501,820],{"className":32502},[127,164],[60,32504,32505,32508],{"style":608},[60,32506],{"className":32507,"style":325},[156],[60,32509,32511],{"className":32510},[161,162,163,164],[60,32512,32514],{"className":32513},[127,164],[60,32515,557],{"className":32516},[127,164],[60,32518,213],{"className":32519},[212],[60,32521,32523],{"className":32522},[144],[60,32524,32526],{"className":32525,"style":17446},[148],[60,32527],{},[60,32529],{"className":32530,"style":470},[469],[60,32532,448],{"className":32533},[474],[60,32535],{"className":32536,"style":470},[469],[60,32538,32540,32543,32546,32600,32603,32606,32609],{"className":32539},[118],[60,32541],{"className":32542,"style":17392},[122],[60,32544,817],{"className":32545},[127],[60,32547,32549,32552],{"className":32548},[127],[60,32550,20410],{"className":32551},[127,178],[60,32553,32555],{"className":32554},[183],[60,32556,32558,32592],{"className":32557},[139,140],[60,32559,32561,32589],{"className":32560},[144],[60,32562,32564,32575],{"className":32563,"style":605},[148],[60,32565,32566,32569],{"style":17413},[60,32567],{"className":32568,"style":325},[156],[60,32570,32572],{"className":32571},[161,162,163,164],[60,32573,814],{"className":32574},[127,164],[60,32576,32577,32580],{"style":608},[60,32578],{"className":32579,"style":325},[156],[60,32581,32583],{"className":32582},[161,162,163,164],[60,32584,32586],{"className":32585},[127,164],[60,32587,557],{"className":32588},[127,164],[60,32590,213],{"className":32591},[212],[60,32593,32595],{"className":32594},[144],[60,32596,32598],{"className":32597,"style":17446},[148],[60,32599],{},[60,32601],{"className":32602,"style":653},[469],[60,32604,1462],{"className":32605},[1495],[60,32607],{"className":32608,"style":653},[469],[60,32610,2152],{"className":32611},[127,178],"。\n代入第二式：\n",[60,32614,32616,32682],{"className":32615},[63],[60,32617,32619],{"className":32618},[67],[69,32620,32621],{"xmlns":71},[73,32622,32623,32679],{},[76,32624,32625,32627,32635,32637,32639,32641,32643,32651,32653,32655,32657,32659,32667,32669,32675,32677],{},[397,32626,817],{},[2127,32628,32629,32631,32633],{},[84,32630,20410],{},[102,32632,814],{},[397,32634,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,32636,1462],{},[397,32638,1465],{},[84,32640,2152],{},[397,32642,990],{},[2127,32644,32645,32647,32649],{},[84,32646,20410],{},[102,32648,814],{},[397,32650,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,32652,1462],{},[397,32654,1465],{},[84,32656,2152],{},[397,32658,990],{},[2127,32660,32661,32663,32665],{},[84,32662,20410],{},[102,32664,814],{},[397,32666,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,32668,448],{},[79,32670,32671,32673],{},[102,32672,30092],{},[84,32674,2152],{},[397,32676,990],{},[102,32678,30099],{},[106,32680,32681],{"encoding":108},"-c_2' \\ln t + c_2' \\ln t + c_2' = \\frac{6}{t} + 34",[60,32683,32685,32769,32850,32919,33002],{"className":32684,"ariaHidden":114},[113],[60,32686,32688,32691,32694,32748,32751,32754,32757,32760,32763,32766],{"className":32687},[118],[60,32689],{"className":32690,"style":17392},[122],[60,32692,817],{"className":32693},[127],[60,32695,32697,32700],{"className":32696},[127],[60,32698,20410],{"className":32699},[127,178],[60,32701,32703],{"className":32702},[183],[60,32704,32706,32740],{"className":32705},[139,140],[60,32707,32709,32737],{"className":32708},[144],[60,32710,32712,32723],{"className":32711,"style":605},[148],[60,32713,32714,32717],{"style":17413},[60,32715],{"className":32716,"style":325},[156],[60,32718,32720],{"className":32719},[161,162,163,164],[60,32721,814],{"className":32722},[127,164],[60,32724,32725,32728],{"style":608},[60,32726],{"className":32727,"style":325},[156],[60,32729,32731],{"className":32730},[161,162,163,164],[60,32732,32734],{"className":32733},[127,164],[60,32735,557],{"className":32736},[127,164],[60,32738,213],{"className":32739},[212],[60,32741,32743],{"className":32742},[144],[60,32744,32746],{"className":32745,"style":17446},[148],[60,32747],{},[60,32749],{"className":32750,"style":653},[469],[60,32752,1462],{"className":32753},[1495],[60,32755],{"className":32756,"style":653},[469],[60,32758,2152],{"className":32759},[127,178],[60,32761],{"className":32762,"style":924},[469],[60,32764,990],{"className":32765},[928],[60,32767],{"className":32768,"style":924},[469],[60,32770,32772,32775,32829,32832,32835,32838,32841,32844,32847],{"className":32771},[118],[60,32773],{"className":32774,"style":17392},[122],[60,32776,32778,32781],{"className":32777},[127],[60,32779,20410],{"className":32780},[127,178],[60,32782,32784],{"className":32783},[183],[60,32785,32787,32821],{"className":32786},[139,140],[60,32788,32790,32818],{"className":32789},[144],[60,32791,32793,32804],{"className":32792,"style":605},[148],[60,32794,32795,32798],{"style":17413},[60,32796],{"className":32797,"style":325},[156],[60,32799,32801],{"className":32800},[161,162,163,164],[60,32802,814],{"className":32803},[127,164],[60,32805,32806,32809],{"style":608},[60,32807],{"className":32808,"style":325},[156],[60,32810,32812],{"className":32811},[161,162,163,164],[60,32813,32815],{"className":32814},[127,164],[60,32816,557],{"className":32817},[127,164],[60,32819,213],{"className":32820},[212],[60,32822,32824],{"className":32823},[144],[60,32825,32827],{"className":32826,"style":17446},[148],[60,32828],{},[60,32830],{"className":32831,"style":653},[469],[60,32833,1462],{"className":32834},[1495],[60,32836],{"className":32837,"style":653},[469],[60,32839,2152],{"className":32840},[127,178],[60,32842],{"className":32843,"style":924},[469],[60,32845,990],{"className":32846},[928],[60,32848],{"className":32849,"style":924},[469],[60,32851,32853,32856,32910,32913,32916],{"className":32852},[118],[60,32854],{"className":32855,"style":17392},[122],[60,32857,32859,32862],{"className":32858},[127],[60,32860,20410],{"className":32861},[127,178],[60,32863,32865],{"className":32864},[183],[60,32866,32868,32902],{"className":32867},[139,140],[60,32869,32871,32899],{"className":32870},[144],[60,32872,32874,32885],{"className":32873,"style":605},[148],[60,32875,32876,32879],{"style":17413},[60,32877],{"className":32878,"style":325},[156],[60,32880,32882],{"className":32881},[161,162,163,164],[60,32883,814],{"className":32884},[127,164],[60,32886,32887,32890],{"style":608},[60,32888],{"className":32889,"style":325},[156],[60,32891,32893],{"className":32892},[161,162,163,164],[60,32894,32896],{"className":32895},[127,164],[60,32897,557],{"className":32898},[127,164],[60,32900,213],{"className":32901},[212],[60,32903,32905],{"className":32904},[144],[60,32906,32908],{"className":32907,"style":17446},[148],[60,32909],{},[60,32911],{"className":32912,"style":470},[469],[60,32914,448],{"className":32915},[474],[60,32917],{"className":32918,"style":470},[469],[60,32920,32922,32925,32993,32996,32999],{"className":32921},[118],[60,32923],{"className":32924,"style":12028},[122],[60,32926,32928,32931,32990],{"className":32927},[127],[60,32929],{"className":32930},[131,132],[60,32932,32934],{"className":32933},[79],[60,32935,32937,32982],{"className":32936},[139,140],[60,32938,32940,32979],{"className":32939},[144],[60,32941,32943,32957,32965],{"className":32942,"style":11547},[148],[60,32944,32945,32948],{"style":152},[60,32946],{"className":32947,"style":157},[156],[60,32949,32951],{"className":32950},[161,162,163,164],[60,32952,32954],{"className":32953},[127,164],[60,32955,2152],{"className":32956},[127,178,164],[60,32958,32959,32962],{"style":225},[60,32960],{"className":32961,"style":157},[156],[60,32963],{"className":32964,"style":233},[232],[60,32966,32967,32970],{"style":1105},[60,32968],{"className":32969,"style":157},[156],[60,32971,32973],{"className":32972},[161,162,163,164],[60,32974,32976],{"className":32975},[127,164],[60,32977,30092],{"className":32978},[127,164],[60,32980,213],{"className":32981},[212],[60,32983,32985],{"className":32984},[144],[60,32986,32988],{"className":32987,"style":3907},[148],[60,32989],{},[60,32991],{"className":32992},[267,132],[60,32994],{"className":32995,"style":924},[469],[60,32997,990],{"className":32998},[928],[60,33000],{"className":33001,"style":924},[469],[60,33003,33005,33008],{"className":33004},[118],[60,33006],{"className":33007,"style":484},[122],[60,33009,30099],{"className":33010},[127],[60,33012,33014,33052],{"className":33013},[63],[60,33015,33017],{"className":33016},[67],[69,33018,33019],{"xmlns":71},[73,33020,33021,33049],{},[76,33022,33023,33025,33027,33029,33037,33039,33045,33047],{},[13095,33024,18294],{},[397,33026,18297],{},[13095,33028,18294],{},[2127,33030,33031,33033,33035],{},[84,33032,20410],{},[102,33034,814],{},[397,33036,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,33038,448],{},[79,33040,33041,33043],{},[102,33042,30092],{},[84,33044,2152],{},[397,33046,990],{},[102,33048,30099],{},[106,33050,33051],{"encoding":108},"\\implies c_2' = \\frac{6}{t} + 34",[60,33053,33055,33073,33142,33225],{"className":33054,"ariaHidden":114},[113],[60,33056,33058,33061,33064,33067,33070],{"className":33057},[118],[60,33059],{"className":33060,"style":18338},[122],[60,33062],{"className":33063,"style":470},[469],[60,33065,18297],{"className":33066},[474],[60,33068],{"className":33069,"style":470},[469],[60,33071],{"className":33072,"style":470},[469],[60,33074,33076,33079,33133,33136,33139],{"className":33075},[118],[60,33077],{"className":33078,"style":17392},[122],[60,33080,33082,33085],{"className":33081},[127],[60,33083,20410],{"className":33084},[127,178],[60,33086,33088],{"className":33087},[183],[60,33089,33091,33125],{"className":33090},[139,140],[60,33092,33094,33122],{"className":33093},[144],[60,33095,33097,33108],{"className":33096,"style":605},[148],[60,33098,33099,33102],{"style":17413},[60,33100],{"className":33101,"style":325},[156],[60,33103,33105],{"className":33104},[161,162,163,164],[60,33106,814],{"className":33107},[127,164],[60,33109,33110,33113],{"style":608},[60,33111],{"className":33112,"style":325},[156],[60,33114,33116],{"className":33115},[161,162,163,164],[60,33117,33119],{"className":33118},[127,164],[60,33120,557],{"className":33121},[127,164],[60,33123,213],{"className":33124},[212],[60,33126,33128],{"className":33127},[144],[60,33129,33131],{"className":33130,"style":17446},[148],[60,33132],{},[60,33134],{"className":33135,"style":470},[469],[60,33137,448],{"className":33138},[474],[60,33140],{"className":33141,"style":470},[469],[60,33143,33145,33148,33216,33219,33222],{"className":33144},[118],[60,33146],{"className":33147,"style":12028},[122],[60,33149,33151,33154,33213],{"className":33150},[127],[60,33152],{"className":33153},[131,132],[60,33155,33157],{"className":33156},[79],[60,33158,33160,33205],{"className":33159},[139,140],[60,33161,33163,33202],{"className":33162},[144],[60,33164,33166,33180,33188],{"className":33165,"style":11547},[148],[60,33167,33168,33171],{"style":152},[60,33169],{"className":33170,"style":157},[156],[60,33172,33174],{"className":33173},[161,162,163,164],[60,33175,33177],{"className":33176},[127,164],[60,33178,2152],{"className":33179},[127,178,164],[60,33181,33182,33185],{"style":225},[60,33183],{"className":33184,"style":157},[156],[60,33186],{"className":33187,"style":233},[232],[60,33189,33190,33193],{"style":1105},[60,33191],{"className":33192,"style":157},[156],[60,33194,33196],{"className":33195},[161,162,163,164],[60,33197,33199],{"className":33198},[127,164],[60,33200,30092],{"className":33201},[127,164],[60,33203,213],{"className":33204},[212],[60,33206,33208],{"className":33207},[144],[60,33209,33211],{"className":33210,"style":3907},[148],[60,33212],{},[60,33214],{"className":33215},[267,132],[60,33217],{"className":33218,"style":924},[469],[60,33220,990],{"className":33221},[928],[60,33223],{"className":33224,"style":924},[469],[60,33226,33228,33231],{"className":33227},[118],[60,33229],{"className":33230,"style":484},[122],[60,33232,30099],{"className":33233},[127],[23,33235,33236,33237,12545,33322],{},"回代求 ",[60,33238,33240,33259],{"className":33239},[63],[60,33241,33243],{"className":33242},[67],[69,33244,33245],{"xmlns":71},[73,33246,33247,33257],{},[76,33248,33249],{},[2127,33250,33251,33253,33255],{},[84,33252,20410],{},[102,33254,820],{},[397,33256,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,33258,27660],{"encoding":108},[60,33260,33262],{"className":33261,"ariaHidden":114},[113],[60,33263,33265,33268],{"className":33264},[118],[60,33266],{"className":33267,"style":17392},[122],[60,33269,33271,33274],{"className":33270},[127],[60,33272,20410],{"className":33273},[127,178],[60,33275,33277],{"className":33276},[183],[60,33278,33280,33314],{"className":33279},[139,140],[60,33281,33283,33311],{"className":33282},[144],[60,33284,33286,33297],{"className":33285,"style":605},[148],[60,33287,33288,33291],{"style":17413},[60,33289],{"className":33290,"style":325},[156],[60,33292,33294],{"className":33293},[161,162,163,164],[60,33295,820],{"className":33296},[127,164],[60,33298,33299,33302],{"style":608},[60,33300],{"className":33301,"style":325},[156],[60,33303,33305],{"className":33304},[161,162,163,164],[60,33306,33308],{"className":33307},[127,164],[60,33309,557],{"className":33310},[127,164],[60,33312,213],{"className":33313},[212],[60,33315,33317],{"className":33316},[144],[60,33318,33320],{"className":33319,"style":17446},[148],[60,33321],{},[60,33323,33325,33395],{"className":33324},[63],[60,33326,33328],{"className":33327},[67],[69,33329,33330],{"xmlns":71},[73,33331,33332,33392],{},[76,33333,33334,33342,33344,33346,33348,33354,33356,33358,33360,33362,33364,33366,33368,33370,33376,33378,33380,33382,33384,33386,33388,33390],{},[2127,33335,33336,33338,33340],{},[84,33337,20410],{},[102,33339,820],{},[397,33341,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,33343,448],{},[397,33345,817],{},[397,33347,400],{"stretchy":399},[79,33349,33350,33352],{},[102,33351,30092],{},[84,33353,2152],{},[397,33355,990],{},[102,33357,30099],{},[397,33359,405],{"stretchy":399},[84,33361,1462],{},[397,33363,1465],{},[84,33365,2152],{},[397,33367,448],{},[397,33369,817],{},[79,33371,33372,33374],{},[102,33373,30092],{},[84,33375,2152],{},[84,33377,1462],{},[397,33379,1465],{},[84,33381,2152],{},[397,33383,817],{},[102,33385,30099],{},[84,33387,1462],{},[397,33389,1465],{},[84,33391,2152],{},[106,33393,33394],{"encoding":108},"c_1' = -(\\frac{6}{t} + 34)\\ln t = -\\frac{6}{t}\\ln t - 34\\ln t",[60,33396,33398,33467,33556,33589,33687],{"className":33397,"ariaHidden":114},[113],[60,33399,33401,33404,33458,33461,33464],{"className":33400},[118],[60,33402],{"className":33403,"style":17392},[122],[60,33405,33407,33410],{"className":33406},[127],[60,33408,20410],{"className":33409},[127,178],[60,33411,33413],{"className":33412},[183],[60,33414,33416,33450],{"className":33415},[139,140],[60,33417,33419,33447],{"className":33418},[144],[60,33420,33422,33433],{"className":33421,"style":605},[148],[60,33423,33424,33427],{"style":17413},[60,33425],{"className":33426,"style":325},[156],[60,33428,33430],{"className":33429},[161,162,163,164],[60,33431,820],{"className":33432},[127,164],[60,33434,33435,33438],{"style":608},[60,33436],{"className":33437,"style":325},[156],[60,33439,33441],{"className":33440},[161,162,163,164],[60,33442,33444],{"className":33443},[127,164],[60,33445,557],{"className":33446},[127,164],[60,33448,213],{"className":33449},[212],[60,33451,33453],{"className":33452},[144],[60,33454,33456],{"className":33455,"style":17446},[148],[60,33457],{},[60,33459],{"className":33460,"style":470},[469],[60,33462,448],{"className":33463},[474],[60,33465],{"className":33466,"style":470},[469],[60,33468,33470,33473,33476,33479,33547,33550,33553],{"className":33469},[118],[60,33471],{"className":33472,"style":12028},[122],[60,33474,817],{"className":33475},[127],[60,33477,400],{"className":33478},[131],[60,33480,33482,33485,33544],{"className":33481},[127],[60,33483],{"className":33484},[131,132],[60,33486,33488],{"className":33487},[79],[60,33489,33491,33536],{"className":33490},[139,140],[60,33492,33494,33533],{"className":33493},[144],[60,33495,33497,33511,33519],{"className":33496,"style":11547},[148],[60,33498,33499,33502],{"style":152},[60,33500],{"className":33501,"style":157},[156],[60,33503,33505],{"className":33504},[161,162,163,164],[60,33506,33508],{"className":33507},[127,164],[60,33509,2152],{"className":33510},[127,178,164],[60,33512,33513,33516],{"style":225},[60,33514],{"className":33515,"style":157},[156],[60,33517],{"className":33518,"style":233},[232],[60,33520,33521,33524],{"style":1105},[60,33522],{"className":33523,"style":157},[156],[60,33525,33527],{"className":33526},[161,162,163,164],[60,33528,33530],{"className":33529},[127,164],[60,33531,30092],{"className":33532},[127,164],[60,33534,213],{"className":33535},[212],[60,33537,33539],{"className":33538},[144],[60,33540,33542],{"className":33541,"style":3907},[148],[60,33543],{},[60,33545],{"className":33546},[267,132],[60,33548],{"className":33549,"style":924},[469],[60,33551,990],{"className":33552},[928],[60,33554],{"className":33555,"style":924},[469],[60,33557,33559,33562,33565,33568,33571,33574,33577,33580,33583,33586],{"className":33558},[118],[60,33560],{"className":33561,"style":418},[122],[60,33563,30099],{"className":33564},[127],[60,33566,405],{"className":33567},[267],[60,33569],{"className":33570,"style":653},[469],[60,33572,1462],{"className":33573},[1495],[60,33575],{"className":33576,"style":653},[469],[60,33578,2152],{"className":33579},[127,178],[60,33581],{"className":33582,"style":470},[469],[60,33584,448],{"className":33585},[474],[60,33587],{"className":33588,"style":470},[469],[60,33590,33592,33595,33598,33666,33669,33672,33675,33678,33681,33684],{"className":33591},[118],[60,33593],{"className":33594,"style":12028},[122],[60,33596,817],{"className":33597},[127],[60,33599,33601,33604,33663],{"className":33600},[127],[60,33602],{"className":33603},[131,132],[60,33605,33607],{"className":33606},[79],[60,33608,33610,33655],{"className":33609},[139,140],[60,33611,33613,33652],{"className":33612},[144],[60,33614,33616,33630,33638],{"className":33615,"style":11547},[148],[60,33617,33618,33621],{"style":152},[60,33619],{"className":33620,"style":157},[156],[60,33622,33624],{"className":33623},[161,162,163,164],[60,33625,33627],{"className":33626},[127,164],[60,33628,2152],{"className":33629},[127,178,164],[60,33631,33632,33635],{"style":225},[60,33633],{"className":33634,"style":157},[156],[60,33636],{"className":33637,"style":233},[232],[60,33639,33640,33643],{"style":1105},[60,33641],{"className":33642,"style":157},[156],[60,33644,33646],{"className":33645},[161,162,163,164],[60,33647,33649],{"className":33648},[127,164],[60,33650,30092],{"className":33651},[127,164],[60,33653,213],{"className":33654},[212],[60,33656,33658],{"className":33657},[144],[60,33659,33661],{"className":33660,"style":3907},[148],[60,33662],{},[60,33664],{"className":33665},[267,132],[60,33667],{"className":33668,"style":653},[469],[60,33670,1462],{"className":33671},[1495],[60,33673],{"className":33674,"style":653},[469],[60,33676,2152],{"className":33677},[127,178],[60,33679],{"className":33680,"style":924},[469],[60,33682,817],{"className":33683},[928],[60,33685],{"className":33686,"style":924},[469],[60,33688,33690,33693,33696,33699,33702,33705],{"className":33689},[118],[60,33691],{"className":33692,"style":13418},[122],[60,33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4: 积分",[51,33714,33715,33854],{},[33,33716,33717],{},[60,33718,33720,33754],{"className":33719},[63],[60,33721,33723],{"className":33722},[67],[69,33724,33725],{"xmlns":71},[73,33726,33727,33751],{},[76,33728,33729,33735,33737,33739,33741,33743,33745,33747,33749],{},[96,33730,33731,33733],{},[84,33732,20410],{},[102,33734,814],{},[397,33736,448],{},[102,33738,30092],{},[84,33740,1462],{},[397,33742,1465],{},[84,33744,2152],{},[397,33746,990],{},[102,33748,30099],{},[84,33750,2152],{},[106,33752,33753],{"encoding":108},"c_2 = 6\\ln t + 34t",[60,33755,33757,33812,33842],{"className":33756,"ariaHidden":114},[113],[60,33758,33760,33763,33803,33806,33809],{"className":33759},[118],[60,33761],{"className":33762,"style":2734},[122],[60,33764,33766,33769],{"className":33765},[127],[60,33767,20410],{"className":33768},[127,178],[60,33770,33772],{"className":33771},[183],[60,33773,33775,33795],{"className":33774},[139,140],[60,33776,33778,33792],{"className":33777},[144],[60,33779,33781],{"className":33780,"style":318},[148],[60,33782,33783,33786],{"style":1940},[60,33784],{"className":33785,"style":325},[156],[60,33787,33789],{"className":33788},[161,162,163,164],[60,33790,814],{"className":33791},[127,164],[60,33793,213],{"className":33794},[212],[60,33796,33798],{"className":33797},[144],[60,33799,33801],{"className":33800,"style":341},[148],[60,33802],{},[60,33804],{"className":33805,"style":470},[469],[60,33807,448],{"className":33808},[474],[60,33810],{"className":33811,"style":470},[469],[60,33813,33815,33818,33821,33824,33827,33830,33833,33836,33839],{"className":33814},[118],[60,33816],{"className":33817,"style":31816},[122],[60,33819,30092],{"className":33820},[127],[60,33822],{"className":33823,"style":653},[469],[60,33825,1462],{"className":33826},[1495],[60,33828],{"className":33829,"style":653},[469],[60,33831,2152],{"className":33832},[127,178],[60,33834],{"className":33835,"style":924},[469],[60,33837,990],{"className":33838},[928],[60,33840],{"className":33841,"style":924},[469],[60,33843,33845,33848,33851],{"className":33844},[118],[60,33846],{"className":33847,"style":484},[122],[60,33849,30099],{"className":33850},[127],[60,33852,2152],{"className":33853},[127,178],[33,33855,33856,34083],{},[60,33857,33859,33915],{"className":33858},[63],[60,33860,33862],{"className":33861},[67],[69,33863,33864],{"xmlns":71},[73,33865,33866,33912],{},[76,33867,33868,33874,33876,33878,33880,33890,33892,33894,33896,33898,33900,33902,33904,33906,33908,33910],{},[96,33869,33870,33872],{},[84,33871,20410],{},[102,33873,820],{},[397,33875,448],{},[397,33877,817],{},[102,33879,1474],{},[550,33881,33882,33888],{},[76,33883,33884,33886],{},[84,33885,1462],{},[397,33887,1465],{},[102,33889,814],{},[84,33891,2152],{},[397,33893,817],{},[102,33895,30099],{},[397,33897,400],{"stretchy":399},[84,33899,2152],{},[84,33901,1462],{},[397,33903,1465],{},[84,33905,2152],{},[397,33907,817],{},[84,33909,2152],{},[397,33911,405],{"stretchy":399},[106,33913,33914],{"encoding":108},"c_1 = -3\\ln^2 t - 34(t\\ln t - t)",[60,33916,33918,33973,34035,34071],{"className":33917,"ariaHidden":114},[113],[60,33919,33921,33924,33964,33967,33970],{"className":33920},[118],[60,33922],{"className":33923,"style":2734},[122],[60,33925,33927,33930],{"className":33926},[127],[60,33928,20410],{"className":33929},[127,178],[60,33931,33933],{"className":33932},[183],[60,33934,33936,33956],{"className":33935},[139,140],[60,33937,33939,33953],{"className":33938},[144],[60,33940,33942],{"className":33941,"style":318},[148],[60,33943,33944,33947],{"style":1940},[60,33945],{"className":33946,"style":325},[156],[60,33948,33950],{"className":33949},[161,162,163,164],[60,33951,820],{"className":33952},[127,164],[60,33954,213],{"className":33955},[212],[60,33957,33959],{"className":33958},[144],[60,33960,33962],{"className":33961,"style":341},[148],[60,33963],{},[60,33965],{"className":33966,"style":470},[469],[60,33968,448],{"className":33969},[474],[60,33971],{"className":33972,"style":470},[469],[60,33974,33976,33980,33983,33986,33989,34020,34023,34026,34029,34032],{"className":33975},[118],[60,33977],{"className":33978,"style":33979},[122],"height:0.9818em;vertical-align:-0.0833em;",[60,33981,817],{"className":33982},[127],[60,33984,1474],{"className":33985},[127],[60,33987],{"className":33988,"style":653},[469],[60,33990,33992,33995],{"className":33991},[1495],[60,33993,1462],{"className":33994},[1495],[60,33996,33998],{"className":33997},[183],[60,33999,34001],{"className":34000},[139],[60,34002,34004],{"className":34003},[144],[60,34005,34008],{"className":34006,"style":34007},[148],"height:0.8984em;",[60,34009,34011,34014],{"style":34010},"top:-3.1473em;margin-right:0.05em;",[60,34012],{"className":34013,"style":325},[156],[60,34015,34017],{"className":34016},[161,162,163,164],[60,34018,814],{"className":34019},[127,164],[60,34021],{"className":34022,"style":653},[469],[60,34024,2152],{"className":34025},[127,178],[60,34027],{"className":34028,"style":924},[469],[60,34030,817],{"className":34031},[928],[60,34033],{"className":34034,"style":924},[469],[60,34036,34038,34041,34044,34047,34050,34053,34056,34059,34062,34065,34068],{"className":34037},[118],[60,34039],{"className":34040,"style":418},[122],[60,34042,30099],{"className":34043},[127],[60,34045,400],{"className":34046},[131],[60,34048,2152],{"className":34049},[127,178],[60,34051],{"className":34052,"style":653},[469],[60,34054,1462],{"className":34055},[1495],[60,34057],{"className":34058,"style":653},[469],[60,34060,2152],{"className":34061},[127,178],[60,34063],{"className":34064,"style":924},[469],[60,34066,817],{"className":34067},[928],[60,34069],{"className":34070,"style":924},[469],[60,34072,34074,34077,34080],{"className":34073},[118],[60,34075],{"className":34076,"style":418},[122],[60,34078,2152],{"className":34079},[127,178],[60,34081,405],{"className":34082},[267]," （分部积分）",[23,34085,34086,5826,34089,7417,34213,34398],{},[26,34087,34088],{},"Step 5: 组合通解",[60,34090,34092,34118],{"className":34091},[63],[60,34093,34095],{"className":34094},[67],[69,34096,34097],{"xmlns":71},[73,34098,34099,34115],{},[76,34100,34101,34107,34109],{},[96,34102,34103,34105],{},[84,34104,20410],{},[102,34106,820],{},[397,34108,569],{"separator":114},[96,34110,34111,34113],{},[84,34112,20410],{},[102,34114,814],{},[106,34116,34117],{"encoding":108},"c_1, c_2",[60,34119,34121],{"className":34120,"ariaHidden":114},[113],[60,34122,34124,34127,34167,34170,34173],{"className":34123},[118],[60,34125],{"className":34126,"style":299},[122],[60,34128,34130,34133],{"className":34129},[127],[60,34131,20410],{"className":34132},[127,178],[60,34134,34136],{"className":34135},[183],[60,34137,34139,34159],{"className":34138},[139,140],[60,34140,34142,34156],{"className":34141},[144],[60,34143,34145],{"className":34144,"style":318},[148],[60,34146,34147,34150],{"style":1940},[60,34148],{"className":34149,"style":325},[156],[60,34151,34153],{"className":34152},[161,162,163,164],[60,34154,820],{"className":34155},[127,164],[60,34157,213],{"className":34158},[212],[60,34160,34162],{"className":34161},[144],[60,34163,34165],{"className":34164,"style":341},[148],[60,34166],{},[60,34168,569],{"className":34169},[649],[60,34171],{"className":34172,"style":653},[469],[60,34174,34176,34179],{"className":34175},[127],[60,34177,20410],{"className":34178},[127,178],[60,34180,34182],{"className":34181},[183],[60,34183,34185,34205],{"className":34184},[139,140],[60,34186,34188,34202],{"className":34187},[144],[60,34189,34191],{"className":34190,"style":318},[148],[60,34192,34193,34196],{"style":1940},[60,34194],{"className":34195,"style":325},[156],[60,34197,34199],{"className":34198},[161,162,163,164],[60,34200,814],{"className":34201},[127,164],[60,34203,213],{"className":34204},[212],[60,34206,34208],{"className":34207},[144],[60,34209,34211],{"className":34210,"style":341},[148],[60,34212],{},[60,34214,34216,34256],{"className":34215},[63],[60,34217,34219],{"className":34218},[67],[69,34220,34221],{"xmlns":71},[73,34222,34223,34253],{},[76,34224,34225,34227,34229,34235,34237,34239,34245,34247,34249,34251],{},[84,34226,359],{},[397,34228,448],{},[96,34230,34231,34233],{},[84,34232,20410],{},[102,34234,820],{},[84,34236,2152],{},[397,34238,990],{},[96,34240,34241,34243],{},[84,34242,20410],{},[102,34244,814],{},[84,34246,2152],{},[84,34248,1462],{},[397,34250,1465],{},[84,34252,2152],{},[106,34254,34255],{"encoding":108},"x = c_1 t + c_2 t\\ln t",[60,34257,34259,34277,34336],{"className":34258,"ariaHidden":114},[113],[60,34260,34262,34265,34268,34271,34274],{"className":34261},[118],[60,34263],{"className":34264,"style":371},[122],[60,34266,359],{"className":34267},[127,178],[60,34269],{"className":34270,"style":470},[469],[60,34272,448],{"className":34273},[474],[60,34275],{"className":34276,"style":470},[469],[60,34278,34280,34284,34324,34327,34330,34333],{"className":34279},[118],[60,34281],{"className":34282,"style":34283},[122],"height:0.7651em;vertical-align:-0.15em;",[60,34285,34287,34290],{"className":34286},[127],[60,34288,20410],{"className":34289},[127,178],[60,34291,34293],{"className":34292},[183],[60,34294,34296,34316],{"className":34295},[139,140],[60,34297,34299,34313],{"className":34298},[144],[60,34300,34302],{"className":34301,"style":318},[148],[60,34303,34304,34307],{"style":1940},[60,34305],{"className":34306,"style":325},[156],[60,34308,34310],{"className":34309},[161,162,163,164],[60,34311,820],{"className":34312},[127,164],[60,34314,213],{"className":34315},[212],[60,34317,34319],{"className":34318},[144],[60,34320,34322],{"className":34321,"style":341},[148],[60,34323],{},[60,34325,2152],{"className":34326},[127,178],[60,34328],{"className":34329,"style":924},[469],[60,34331,990],{"className":34332},[928],[60,34334],{"className":34335,"style":924},[469],[60,34337,34339,34343,34383,34386,34389,34392,34395],{"className":34338},[118],[60,34340],{"className":34341,"style":34342},[122],"height:0.8444em;vertical-align:-0.15em;",[60,34344,34346,34349],{"className":34345},[127],[60,34347,20410],{"className":34348},[127,178],[60,34350,34352],{"className":34351},[183],[60,34353,34355,34375],{"className":34354},[139,140],[60,34356,34358,34372],{"className":34357},[144],[60,34359,34361],{"className":34360,"style":318},[148],[60,34362,34363,34366],{"style":1940},[60,34364],{"className":34365,"style":325},[156],[60,34367,34369],{"className":34368},[161,162,163,164],[60,34370,814],{"className":34371},[127,164],[60,34373,213],{"className":34374},[212],[60,34376,34378],{"className":34377},[144],[60,34379,34381],{"className":34380,"style":341},[148],[60,34382],{},[60,34384,2152],{"className":34385},[127,178],[60,34387],{"className":34388,"style":653},[469],[60,34390,1462],{"className":34391},[1495],[60,34393],{"className":34394,"style":653},[469],[60,34396,2152],{"className":34397},[127,178]," 整理即可。",[15,34400],{},[18,34402,34404],{"id":34403},"_4-归一化基本解组标准基本解组","4. 归一化基本解组（标准基本解组）",[23,34406,34407,34410,34411,9555,34523,34574,34575,9401,34661,34746],{},[26,34408,34409],{},"题目意思：","\n现在的基本解组 ",[60,34412,34414,34444],{"className":34413},[63],[60,34415,34417],{"className":34416},[67],[69,34418,34419],{"xmlns":71},[73,34420,34421,34441],{},[76,34422,34423,34429,34431],{},[550,34424,34425,34427],{},[84,34426,981],{},[84,34428,2152],{},[397,34430,569],{"separator":114},[550,34432,34433,34435],{},[84,34434,981],{},[76,34436,34437,34439],{},[397,34438,817],{},[84,34440,2152],{},[106,34442,34443],{"encoding":108},"e^t, e^{-t}",[60,34445,34447],{"className":34446,"ariaHidden":114},[113],[60,34448,34450,34453,34482,34485,34488],{"className":34449},[118],[60,34451],{"className":34452,"style":20113},[122],[60,34454,34456,34459],{"className":34455},[127],[60,34457,981],{"className":34458},[127,178],[60,34460,34462],{"className":34461},[183],[60,34463,34465],{"className":34464},[139],[60,34466,34468],{"className":34467},[144],[60,34469,34471],{"className":34470,"style":20132},[148],[60,34472,34473,34476],{"style":608},[60,34474],{"className":34475,"style":325},[156],[60,34477,34479],{"className":34478},[161,162,163,164],[60,34480,2152],{"className":34481},[127,178,164],[60,34483,569],{"className":34484},[649],[60,34486],{"className":34487,"style":653},[469],[60,34489,34491,34494],{"className":34490},[127],[60,34492,981],{"className":34493},[127,178],[60,34495,34497],{"className":34496},[183],[60,34498,34500],{"className":34499},[139],[60,34501,34503],{"className":34502},[144],[60,34504,34506],{"className":34505,"style":20132},[148],[60,34507,34508,34511],{"style":608},[60,34509],{"className":34510,"style":325},[156],[60,34512,34514],{"className":34513},[161,162,163,164],[60,34515,34517,34520],{"className":34516},[127,164],[60,34518,817],{"className":34519},[127,164],[60,34521,2152],{"className":34522},[127,178,164],[60,34524,34526,34544],{"className":34525},[63],[60,34527,34529],{"className":34528},[67],[69,34530,34531],{"xmlns":71},[73,34532,34533,34541],{},[76,34534,34535,34537,34539],{},[84,34536,2152],{},[397,34538,448],{},[102,34540,104],{},[106,34542,34543],{"encoding":108},"t=0",[60,34545,34547,34565],{"className":34546,"ariaHidden":114},[113],[60,34548,34550,34553,34556,34559,34562],{"className":34549},[118],[60,34551],{"className":34552,"style":6002},[122],[60,34554,2152],{"className":34555},[127,178],[60,34557],{"className":34558,"style":470},[469],[60,34560,448],{"className":34561},[474],[60,34563],{"className":34564,"style":470},[469],[60,34566,34568,34571],{"className":34567},[118],[60,34569],{"className":34570,"style":484},[122],[60,34572,104],{"className":34573},[127]," 时的数值乱七八糟的。\n我们想要两个新的“完美”解 ",[60,34576,34578,34603],{"className":34577},[63],[60,34579,34581],{"className":34580},[67],[69,34582,34583],{"xmlns":71},[73,34584,34585,34600],{},[76,34586,34587,34594,34596,34598],{},[96,34588,34589,34592],{},[84,34590,34591],{},"ϕ",[102,34593,820],{},[397,34595,400],{"stretchy":399},[84,34597,2152],{},[397,34599,405],{"stretchy":399},[106,34601,34602],{"encoding":108},"\\phi_1(t)",[60,34604,34606],{"className":34605,"ariaHidden":114},[113],[60,34607,34609,34612,34652,34655,34658],{"className":34608},[118],[60,34610],{"className":34611,"style":418},[122],[60,34613,34615,34618],{"className":34614},[127],[60,34616,34591],{"className":34617},[127,178],[60,34619,34621],{"className":34620},[183],[60,34622,34624,34644],{"className":34623},[139,140],[60,34625,34627,34641],{"className":34626},[144],[60,34628,34630],{"className":34629,"style":318},[148],[60,34631,34632,34635],{"style":1940},[60,34633],{"className":34634,"style":325},[156],[60,34636,34638],{"className":34637},[161,162,163,164],[60,34639,820],{"className":34640},[127,164],[60,34642,213],{"className":34643},[212],[60,34645,34647],{"className":34646},[144],[60,34648,34650],{"className":34649,"style":341},[148],[60,34651],{},[60,34653,400],{"className":34654},[131],[60,34656,2152],{"className":34657},[127,178],[60,34659,405],{"className":34660},[267],[60,34662,34664,34688],{"className":34663},[63],[60,34665,34667],{"className":34666},[67],[69,34668,34669],{"xmlns":71},[73,34670,34671,34685],{},[76,34672,34673,34679,34681,34683],{},[96,34674,34675,34677],{},[84,34676,34591],{},[102,34678,814],{},[397,34680,400],{"stretchy":399},[84,34682,2152],{},[397,34684,405],{"stretchy":399},[106,34686,34687],{"encoding":108},"\\phi_2(t)",[60,34689,34691],{"className":34690,"ariaHidden":114},[113],[60,34692,34694,34697,34737,34740,34743],{"className":34693},[118],[60,34695],{"className":34696,"style":418},[122],[60,34698,34700,34703],{"className":34699},[127],[60,34701,34591],{"className":34702},[127,178],[60,34704,34706],{"className":34705},[183],[60,34707,34709,34729],{"className":34708},[139,140],[60,34710,34712,34726],{"className":34711},[144],[60,34713,34715],{"className":34714,"style":318},[148],[60,34716,34717,34720],{"style":1940},[60,34718],{"className":34719,"style":325},[156],[60,34721,34723],{"className":34722},[161,162,163,164],[60,34724,814],{"className":34725},[127,164],[60,34727,213],{"className":34728},[212],[60,34730,34732],{"className":34731},[144],[60,34733,34735],{"className":34734,"style":341},[148],[60,34736],{},[60,34738,400],{"className":34739},[131],[60,34741,2152],{"className":34742},[127,178],[60,34744,405],{"className":34745},[267],"，它们满足：",[51,34748,34749,34966],{},[33,34750,34751,34965],{},[60,34752,34754,34802],{"className":34753},[63],[60,34755,34757],{"className":34756},[67],[69,34758,34759],{"xmlns":71},[73,34760,34761,34799],{},[76,34762,34763,34769,34771,34773,34775,34777,34779,34781,34789,34791,34793,34795,34797],{},[96,34764,34765,34767],{},[84,34766,34591],{},[102,34768,820],{},[397,34770,400],{"stretchy":399},[102,34772,104],{},[397,34774,405],{"stretchy":399},[397,34776,448],{},[102,34778,820],{},[397,34780,569],{"separator":114},[2127,34782,34783,34785,34787],{},[84,34784,34591],{},[102,34786,820],{},[397,34788,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,34790,400],{"stretchy":399},[102,34792,104],{},[397,34794,405],{"stretchy":399},[397,34796,448],{},[102,34798,104],{},[106,34800,34801],{"encoding":108},"\\phi_1(0)=1, \\phi_1'(0)=0",[60,34803,34805,34869,34956],{"className":34804,"ariaHidden":114},[113],[60,34806,34808,34811,34851,34854,34857,34860,34863,34866],{"className":34807},[118],[60,34809],{"className":34810,"style":418},[122],[60,34812,34814,34817],{"className":34813},[127],[60,34815,34591],{"className":34816},[127,178],[60,34818,34820],{"className":34819},[183],[60,34821,34823,34843],{"className":34822},[139,140],[60,34824,34826,34840],{"className":34825},[144],[60,34827,34829],{"className":34828,"style":318},[148],[60,34830,34831,34834],{"style":1940},[60,34832],{"className":34833,"style":325},[156],[60,34835,34837],{"className":34836},[161,162,163,164],[60,34838,820],{"className":34839},[127,164],[60,34841,213],{"className":34842},[212],[60,34844,34846],{"className":34845},[144],[60,34847,34849],{"className":34848,"style":341},[148],[60,34850],{},[60,34852,400],{"className":34853},[131],[60,34855,104],{"className":34856},[127],[60,34858,405],{"className":34859},[267],[60,34861],{"className":34862,"style":470},[469],[60,34864,448],{"className":34865},[474],[60,34867],{"className":34868,"style":470},[469],[60,34870,34872,34875,34878,34881,34884,34938,34941,34944,34947,34950,34953],{"className":34871},[118],[60,34873],{"className":34874,"style":10437},[122],[60,34876,820],{"className":34877},[127],[60,34879,569],{"className":34880},[649],[60,34882],{"className":34883,"style":653},[469],[60,34885,34887,34890],{"className":34886},[127],[60,34888,34591],{"className":34889},[127,178],[60,34891,34893],{"className":34892},[183],[60,34894,34896,34930],{"className":34895},[139,140],[60,34897,34899,34927],{"className":34898},[144],[60,34900,34902,34913],{"className":34901,"style":605},[148],[60,34903,34904,34907],{"style":17413},[60,34905],{"className":34906,"style":325},[156],[60,34908,34910],{"className":34909},[161,162,163,164],[60,34911,820],{"className":34912},[127,164],[60,34914,34915,34918],{"style":608},[60,34916],{"className":34917,"style":325},[156],[60,34919,34921],{"className":34920},[161,162,163,164],[60,34922,34924],{"className":34923},[127,164],[60,34925,557],{"className":34926},[127,164],[60,34928,213],{"className":34929},[212],[60,34931,34933],{"className":34932},[144],[60,34934,34936],{"className":34935,"style":17446},[148],[60,34937],{},[60,34939,400],{"className":34940},[131],[60,34942,104],{"className":34943},[127],[60,34945,405],{"className":34946},[267],[60,34948],{"className":34949,"style":470},[469],[60,34951,448],{"className":34952},[474],[60,34954],{"className":34955,"style":470},[469],[60,34957,34959,34962],{"className":34958},[118],[60,34960],{"className":34961,"style":484},[122],[60,34963,104],{"className":34964},[127]," （这叫“位置解”，只管初始位置）",[33,34967,34968,35182],{},[60,34969,34971,35019],{"className":34970},[63],[60,34972,34974],{"className":34973},[67],[69,34975,34976],{"xmlns":71},[73,34977,34978,35016],{},[76,34979,34980,34986,34988,34990,34992,34994,34996,34998,35006,35008,35010,35012,35014],{},[96,34981,34982,34984],{},[84,34983,34591],{},[102,34985,814],{},[397,34987,400],{"stretchy":399},[102,34989,104],{},[397,34991,405],{"stretchy":399},[397,34993,448],{},[102,34995,104],{},[397,34997,569],{"separator":114},[2127,34999,35000,35002,35004],{},[84,35001,34591],{},[102,35003,814],{},[397,35005,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,35007,400],{"stretchy":399},[102,35009,104],{},[397,35011,405],{"stretchy":399},[397,35013,448],{},[102,35015,820],{},[106,35017,35018],{"encoding":108},"\\phi_2(0)=0, \\phi_2'(0)=1",[60,35020,35022,35086,35173],{"className":35021,"ariaHidden":114},[113],[60,35023,35025,35028,35068,35071,35074,35077,35080,35083],{"className":35024},[118],[60,35026],{"className":35027,"style":418},[122],[60,35029,35031,35034],{"className":35030},[127],[60,35032,34591],{"className":35033},[127,178],[60,35035,35037],{"className":35036},[183],[60,35038,35040,35060],{"className":35039},[139,140],[60,35041,35043,35057],{"className":35042},[144],[60,35044,35046],{"className":35045,"style":318},[148],[60,35047,35048,35051],{"style":1940},[60,35049],{"className":35050,"style":325},[156],[60,35052,35054],{"className":35053},[161,162,163,164],[60,35055,814],{"className":35056},[127,164],[60,35058,213],{"className":35059},[212],[60,35061,35063],{"className":35062},[144],[60,35064,35066],{"className":35065,"style":341},[148],[60,35067],{},[60,35069,400],{"className":35070},[131],[60,35072,104],{"className":35073},[127],[60,35075,405],{"className":35076},[267],[60,35078],{"className":35079,"style":470},[469],[60,35081,448],{"className":35082},[474],[60,35084],{"className":35085,"style":470},[469],[60,35087,35089,35092,35095,35098,35101,35155,35158,35161,35164,35167,35170],{"className":35088},[118],[60,35090],{"className":35091,"style":10437},[122],[60,35093,104],{"className":35094},[127],[60,35096,569],{"className":35097},[649],[60,35099],{"className":35100,"style":653},[469],[60,35102,35104,35107],{"className":35103},[127],[60,35105,34591],{"className":35106},[127,178],[60,35108,35110],{"className":35109},[183],[60,35111,35113,35147],{"className":35112},[139,140],[60,35114,35116,35144],{"className":35115},[144],[60,35117,35119,35130],{"className":35118,"style":605},[148],[60,35120,35121,35124],{"style":17413},[60,35122],{"className":35123,"style":325},[156],[60,35125,35127],{"className":35126},[161,162,163,164],[60,35128,814],{"className":35129},[127,164],[60,35131,35132,35135],{"style":608},[60,35133],{"className":35134,"style":325},[156],[60,35136,35138],{"className":35137},[161,162,163,164],[60,35139,35141],{"className":35140},[127,164],[60,35142,557],{"className":35143},[127,164],[60,35145,213],{"className":35146},[212],[60,35148,35150],{"className":35149},[144],[60,35151,35153],{"className":35152,"style":17446},[148],[60,35154],{},[60,35156,400],{"className":35157},[131],[60,35159,104],{"className":35160},[127],[60,35162,405],{"className":35163},[267],[60,35165],{"className":35166,"style":470},[469],[60,35168,448],{"className":35169},[474],[60,35171],{"className":35172,"style":470},[469],[60,35174,35176,35179],{"className":35175},[118],[60,35177],{"className":35178,"style":484},[122],[60,35180,820],{"className":35181},[127]," （这叫“速度解”，只管初始速度）",[23,35184,35185],{},[26,35186,35187],{},"解法：",[23,35189,35190,35263,35264,35555,35556,35943,35944,36250,36251,36546],{},[26,35191,35192,35193],{},"第一步：构造 ",[60,35194,35196,35214],{"className":35195},[63],[60,35197,35199],{"className":35198},[67],[69,35200,35201],{"xmlns":71},[73,35202,35203,35211],{},[76,35204,35205],{},[96,35206,35207,35209],{},[84,35208,34591],{},[102,35210,820],{},[106,35212,35213],{"encoding":108},"\\phi_1",[60,35215,35217],{"className":35216,"ariaHidden":114},[113],[60,35218,35220,35223],{"className":35219},[118],[60,35221],{"className":35222,"style":694},[122],[60,35224,35226,35229],{"className":35225},[127],[60,35227,34591],{"className":35228},[127,178],[60,35230,35232],{"className":35231},[183],[60,35233,35235,35255],{"className":35234},[139,140],[60,35236,35238,35252],{"className":35237},[144],[60,35239,35241],{"className":35240,"style":318},[148],[60,35242,35243,35246],{"style":1940},[60,35244],{"className":35245,"style":325},[156],[60,35247,35249],{"className":35248},[161,162,163,164],[60,35250,820],{"className":35251},[127,164],[60,35253,213],{"className":35254},[212],[60,35256,35258],{"className":35257},[144],[60,35259,35261],{"className":35260,"style":341},[148],[60,35262],{},"\n设 ",[60,35265,35267,35323],{"className":35266},[63],[60,35268,35270],{"className":35269},[67],[69,35271,35272],{"xmlns":71},[73,35273,35274,35320],{},[76,35275,35276,35282,35284,35286,35288,35290,35296,35302,35304,35310],{},[96,35277,35278,35280],{},[84,35279,34591],{},[102,35281,820],{},[397,35283,400],{"stretchy":399},[84,35285,2152],{},[397,35287,405],{"stretchy":399},[397,35289,448],{},[96,35291,35292,35294],{},[84,35293,20410],{},[102,35295,820],{},[550,35297,35298,35300],{},[84,35299,981],{},[84,35301,2152],{},[397,35303,990],{},[96,35305,35306,35308],{},[84,35307,20410],{},[102,35309,814],{},[550,35311,35312,35314],{},[84,35313,981],{},[76,35315,35316,35318],{},[397,35317,817],{},[84,35319,2152],{},[106,35321,35322],{"encoding":108},"\\phi_1(t) = c_1 e^t + c_2 e^{-t}",[60,35324,35326,35390,35474],{"className":35325,"ariaHidden":114},[113],[60,35327,35329,35332,35372,35375,35378,35381,35384,35387],{"className":35328},[118],[60,35330],{"className":35331,"style":418},[122],[60,35333,35335,35338],{"className":35334},[127],[60,35336,34591],{"className":35337},[127,178],[60,35339,35341],{"className":35340},[183],[60,35342,35344,35364],{"className":35343},[139,140],[60,35345,35347,35361],{"className":35346},[144],[60,35348,35350],{"className":35349,"style":318},[148],[60,35351,35352,35355],{"style":1940},[60,35353],{"className":35354,"style":325},[156],[60,35356,35358],{"className":35357},[161,162,163,164],[60,35359,820],{"className":35360},[127,164],[60,35362,213],{"className":35363},[212],[60,35365,35367],{"className":35366},[144],[60,35368,35370],{"className":35369,"style":341},[148],[60,35371],{},[60,35373,400],{"className":35374},[131],[60,35376,2152],{"className":35377},[127,178],[60,35379,405],{"className":35380},[267],[60,35382],{"className":35383,"style":470},[469],[60,35385,448],{"className":35386},[474],[60,35388],{"className":35389,"style":470},[469],[60,35391,35393,35396,35436,35465,35468,35471],{"className":35392},[118],[60,35394],{"className":35395,"style":24622},[122],[60,35397,35399,35402],{"className":35398},[127],[60,35400,20410],{"className":35401},[127,178],[60,35403,35405],{"className":35404},[183],[60,35406,35408,35428],{"className":35407},[139,140],[60,35409,35411,35425],{"className":35410},[144],[60,35412,35414],{"className":35413,"style":318},[148],[60,35415,35416,35419],{"style":1940},[60,35417],{"className":35418,"style":325},[156],[60,35420,35422],{"className":35421},[161,162,163,164],[60,35423,820],{"className":35424},[127,164],[60,35426,213],{"className":35427},[212],[60,35429,35431],{"className":35430},[144],[60,35432,35434],{"className":35433,"style":341},[148],[60,35435],{},[60,35437,35439,35442],{"className":35438},[127],[60,35440,981],{"className":35441},[127,178],[60,35443,35445],{"className":35444},[183],[60,35446,35448],{"className":35447},[139],[60,35449,35451],{"className":35450},[144],[60,35452,35454],{"className":35453,"style":20132},[148],[60,35455,35456,35459],{"style":608},[60,35457],{"className":35458,"style":325},[156],[60,35460,35462],{"className":35461},[161,162,163,164],[60,35463,2152],{"className":35464},[127,178,164],[60,35466],{"className":35467,"style":924},[469],[60,35469,990],{"className":35470},[928],[60,35472],{"className":35473,"style":924},[469],[60,35475,35477,35480,35520],{"className":35476},[118],[60,35478],{"className":35479,"style":24622},[122],[60,35481,35483,35486],{"className":35482},[127],[60,35484,20410],{"className":35485},[127,178],[60,35487,35489],{"className":35488},[183],[60,35490,35492,35512],{"className":35491},[139,140],[60,35493,35495,35509],{"className":35494},[144],[60,35496,35498],{"className":35497,"style":318},[148],[60,35499,35500,35503],{"style":1940},[60,35501],{"className":35502,"style":325},[156],[60,35504,35506],{"className":35505},[161,162,163,164],[60,35507,814],{"className":35508},[127,164],[60,35510,213],{"className":35511},[212],[60,35513,35515],{"className":35514},[144],[60,35516,35518],{"className":35517,"style":341},[148],[60,35519],{},[60,35521,35523,35526],{"className":35522},[127],[60,35524,981],{"className":35525},[127,178],[60,35527,35529],{"className":35528},[183],[60,35530,35532],{"className":35531},[139],[60,35533,35535],{"className":35534},[144],[60,35536,35538],{"className":35537,"style":20132},[148],[60,35539,35540,35543],{"style":608},[60,35541],{"className":35542,"style":325},[156],[60,35544,35546],{"className":35545},[161,162,163,164],[60,35547,35549,35552],{"className":35548},[127,164],[60,35550,817],{"className":35551},[127,164],[60,35553,2152],{"className":35554},[127,178,164],"。\n代入初值条件：\n[\n",[60,35557,35559,35645],{"className":35558},[63],[60,35560,35562],{"className":35561},[67],[69,35563,35564],{"xmlns":71},[73,35565,35566,35642],{},[76,35567,35568,35570],{},[397,35569,20568],{"fence":114},[20570,35571,35572,35607],{"rowspacing":20572,"columnalign":20573,"columnspacing":13091},[20575,35573,35574],{},[20578,35575,35576],{},[20581,35577,35578],{"scriptlevel":104,"displaystyle":399},[76,35579,35580,35586,35588,35594,35596,35598,35600,35602,35605],{},[96,35581,35582,35584],{},[84,35583,20410],{},[102,35585,820],{},[397,35587,990],{},[96,35589,35590,35592],{},[84,35591,20410],{},[102,35593,814],{},[397,35595,448],{},[102,35597,820],{},[469,35599],{"width":13091},[397,35601,400],{"stretchy":399},[13095,35603,35604],{},"函数值",[397,35606,405],{"stretchy":399},[20575,35608,35609],{},[20578,35610,35611],{},[20581,35612,35613],{"scriptlevel":104,"displaystyle":399},[76,35614,35615,35621,35623,35629,35631,35633,35635,35637,35640],{},[96,35616,35617,35619],{},[84,35618,20410],{},[102,35620,820],{},[397,35622,817],{},[96,35624,35625,35627],{},[84,35626,20410],{},[102,35628,814],{},[397,35630,448],{},[102,35632,104],{},[469,35634],{"width":13091},[397,35636,400],{"stretchy":399},[13095,35638,35639],{},"导数值",[397,35641,405],{"stretchy":399},[106,35643,35644],{"encoding":108},"\\begin{cases}\nc_1 + c_2 = 1 \\quad (\\text{函数值}) \\\\\nc_1 - c_2 = 0 \\quad (\\text{导数值})\n\\end{cases}",[60,35646,35648],{"className":35647,"ariaHidden":114},[113],[60,35649,35651,35654],{"className":35650},[118],[60,35652],{"className":35653,"style":20819},[122],[60,35655,35657,35663,35940],{"className":35656},[2326],[60,35658,35660],{"className":35659,"style":2331},[131,2330],[60,35661,20568],{"className":35662},[2335,20829],[60,35664,35666],{"className":35665},[127],[60,35667,35669],{"className":35668},[20570],[60,35670,35672],{"className":35671},[20839],[60,35673,35675,35932],{"className":35674},[139,140],[60,35676,35678,35929],{"className":35677},[144],[60,35679,35681,35805],{"className":35680,"style":20849},[148],[60,35682,35683,35686],{"style":20852},[60,35684],{"className":35685,"style":20856},[156],[60,35687,35689,35729,35732,35735,35738,35778,35781,35784,35787,35790,35793,35796,35802],{"className":35688},[127],[60,35690,35692,35695],{"className":35691},[127],[60,35693,20410],{"className":35694},[127,178],[60,35696,35698],{"className":35697},[183],[60,35699,35701,35721],{"className":35700},[139,140],[60,35702,35704,35718],{"className":35703},[144],[60,35705,35707],{"className":35706,"style":318},[148],[60,35708,35709,35712],{"style":1940},[60,35710],{"className":35711,"style":325},[156],[60,35713,35715],{"className":35714},[161,162,163,164],[60,35716,820],{"className":35717},[127,164],[60,35719,213],{"className":35720},[212],[60,35722,35724],{"className":35723},[144],[60,35725,35727],{"className":35726,"style":341},[148],[60,35728],{},[60,35730],{"className":35731,"style":924},[469],[60,35733,990],{"className":35734},[928],[60,35736],{"className":35737,"style":924},[469],[60,35739,35741,35744],{"className":35740},[127],[60,35742,20410],{"className":35743},[127,178],[60,35745,35747],{"className":35746},[183],[60,35748,35750,35770],{"className":35749},[139,140],[60,35751,35753,35767],{"className":35752},[144],[60,35754,35756],{"className":35755,"style":318},[148],[60,35757,35758,35761],{"style":1940},[60,35759],{"className":35760,"style":325},[156],[60,35762,35764],{"className":35763},[161,162,163,164],[60,35765,814],{"className":35766},[127,164],[60,35768,213],{"className":35769},[212],[60,35771,35773],{"className":35772},[144],[60,35774,35776],{"className":35775,"style":341},[148],[60,35777],{},[60,35779],{"className":35780,"style":470},[469],[60,35782,448],{"className":35783},[474],[60,35785],{"className":35786,"style":470},[469],[60,35788,820],{"className":35789},[127],[60,35791],{"className":35792,"style":13455},[469],[60,35794,400],{"className":35795},[131],[60,35797,35799],{"className":35798},[127,13462],[60,35800,35604],{"className":35801},[127,13466],[60,35803,405],{"className":35804},[267],[60,35806,35807,35810],{"style":21055},[60,35808],{"className":35809,"style":20856},[156],[60,35811,35813,35853,35856,35859,35862,35902,35905,35908,35911,35914,35917,35920,35926],{"className":35812},[127],[60,35814,35816,35819],{"className":35815},[127],[60,35817,20410],{"className":35818},[127,178],[60,35820,35822],{"className":35821},[183],[60,35823,35825,35845],{"className":35824},[139,140],[60,35826,35828,35842],{"className":35827},[144],[60,35829,35831],{"className":35830,"style":318},[148],[60,35832,35833,35836],{"style":1940},[60,35834],{"className":35835,"style":325},[156],[60,35837,35839],{"className":35838},[161,162,163,164],[60,35840,820],{"className":35841},[127,164],[60,35843,213],{"className":35844},[212],[60,35846,35848],{"className":35847},[144],[60,35849,35851],{"className":35850,"style":341},[148],[60,35852],{},[60,35854],{"className":35855,"style":924},[469],[60,35857,817],{"className":35858},[928],[60,35860],{"className":35861,"style":924},[469],[60,35863,35865,35868],{"className":35864},[127],[60,35866,20410],{"className":35867},[127,178],[60,35869,35871],{"className":35870},[183],[60,35872,35874,35894],{"className":35873},[139,140],[60,35875,35877,35891],{"className":35876},[144],[60,35878,35880],{"className":35879,"style":318},[148],[60,35881,35882,35885],{"style":1940},[60,35883],{"className":35884,"style":325},[156],[60,35886,35888],{"className":35887},[161,162,163,164],[60,35889,814],{"className":35890},[127,164],[60,35892,213],{"className":35893},[212],[60,35895,35897],{"className":35896},[144],[60,35898,35900],{"className":35899,"style":341},[148],[60,35901],{},[60,35903],{"className":35904,"style":470},[469],[60,35906,448],{"className":35907},[474],[60,35909],{"className":35910,"style":470},[469],[60,35912,104],{"className":35913},[127],[60,35915],{"className":35916,"style":13455},[469],[60,35918,400],{"className":35919},[131],[60,35921,35923],{"className":35922},[127,13462],[60,35924,35639],{"className":35925},[127,13466],[60,35927,405],{"className":35928},[267],[60,35930,213],{"className":35931},[212],[60,35933,35935],{"className":35934},[144],[60,35936,35938],{"className":35937,"style":21340},[148],[60,35939],{},[60,35941],{"className":35942},[267,132],"\n]\n解得 ",[60,35945,35947,35989],{"className":35946},[63],[60,35948,35950],{"className":35949},[67],[69,35951,35952],{"xmlns":71},[73,35953,35954,35986],{},[76,35955,35956,35962,35964,35970,35972,35978,35980],{},[96,35957,35958,35960],{},[84,35959,20410],{},[102,35961,820],{},[397,35963,448],{},[79,35965,35966,35968],{},[102,35967,820],{},[102,35969,814],{},[397,35971,569],{"separator":114},[96,35973,35974,35976],{},[84,35975,20410],{},[102,35977,814],{},[397,35979,448],{},[79,35981,35982,35984],{},[102,35983,820],{},[102,35985,814],{},[106,35987,35988],{"encoding":108},"c_1 = \\frac{1}{2}, c_2 = \\frac{1}{2}",[60,35990,35992,36047,36176],{"className":35991,"ariaHidden":114},[113],[60,35993,35995,35998,36038,36041,36044],{"className":35994},[118],[60,35996],{"className":35997,"style":2734},[122],[60,35999,36001,36004],{"className":36000},[127],[60,36002,20410],{"className":36003},[127,178],[60,36005,36007],{"className":36006},[183],[60,36008,36010,36030],{"className":36009},[139,140],[60,36011,36013,36027],{"className":36012},[144],[60,36014,36016],{"className":36015,"style":318},[148],[60,36017,36018,36021],{"style":1940},[60,36019],{"className":36020,"style":325},[156],[60,36022,36024],{"className":36023},[161,162,163,164],[60,36025,820],{"className":36026},[127,164],[60,36028,213],{"className":36029},[212],[60,36031,36033],{"className":36032},[144],[60,36034,36036],{"className":36035,"style":341},[148],[60,36037],{},[60,36039],{"className":36040,"style":470},[469],[60,36042,448],{"className":36043},[474],[60,36045],{"className":36046,"style":470},[469],[60,36048,36050,36053,36121,36124,36127,36167,36170,36173],{"className":36049},[118],[60,36051],{"className":36052,"style":12028},[122],[60,36054,36056,36059,36118],{"className":36055},[127],[60,36057],{"className":36058},[131,132],[60,36060,36062],{"className":36061},[79],[60,36063,36065,36110],{"className":36064},[139,140],[60,36066,36068,36107],{"className":36067},[144],[60,36069,36071,36085,36093],{"className":36070,"style":11547},[148],[60,36072,36073,36076],{"style":152},[60,36074],{"className":36075,"style":157},[156],[60,36077,36079],{"className":36078},[161,162,163,164],[60,36080,36082],{"className":36081},[127,164],[60,36083,814],{"className":36084},[127,164],[60,36086,36087,36090],{"style":225},[60,36088],{"className":36089,"style":157},[156],[60,36091],{"className":36092,"style":233},[232],[60,36094,36095,36098],{"style":1105},[60,36096],{"className":36097,"style":157},[156],[60,36099,36101],{"className":36100},[161,162,163,164],[60,36102,36104],{"className":36103},[127,164],[60,36105,820],{"className":36106},[127,164],[60,36108,213],{"className":36109},[212],[60,36111,36113],{"className":36112},[144],[60,36114,36116],{"className":36115,"style":3907},[148],[60,36117],{},[60,36119],{"className":36120},[267,132],[60,36122,569],{"className":36123},[649],[60,36125],{"className":36126,"style":653},[469],[60,36128,36130,36133],{"className":36129},[127],[60,36131,20410],{"className":36132},[127,178],[60,36134,36136],{"className":36135},[183],[60,36137,36139,36159],{"className":36138},[139,140],[60,36140,36142,36156],{"className":36141},[144],[60,36143,36145],{"className":36144,"style":318},[148],[60,36146,36147,36150],{"style":1940},[60,36148],{"className":36149,"style":325},[156],[60,36151,36153],{"className":36152},[161,162,163,164],[60,36154,814],{"className":36155},[127,164],[60,36157,213],{"className":36158},[212],[60,36160,36162],{"className":36161},[144],[60,36163,36165],{"className":36164,"style":341},[148],[60,36166],{},[60,36168],{"className":36169,"style":470},[469],[60,36171,448],{"className":36172},[474],[60,36174],{"className":36175,"style":470},[469],[60,36177,36179,36182],{"className":36178},[118],[60,36180],{"className":36181,"style":12028},[122],[60,36183,36185,36188,36247],{"className":36184},[127],[60,36186],{"className":36187},[131,132],[60,36189,36191],{"className":36190},[79],[60,36192,36194,36239],{"className":36193},[139,140],[60,36195,36197,36236],{"className":36196},[144],[60,36198,36200,36214,36222],{"className":36199,"style":11547},[148],[60,36201,36202,36205],{"style":152},[60,36203],{"className":36204,"style":157},[156],[60,36206,36208],{"className":36207},[161,162,163,164],[60,36209,36211],{"className":36210},[127,164],[60,36212,814],{"className":36213},[127,164],[60,36215,36216,36219],{"style":225},[60,36217],{"className":36218,"style":157},[156],[60,36220],{"className":36221,"style":233},[232],[60,36223,36224,36227],{"style":1105},[60,36225],{"className":36226,"style":157},[156],[60,36228,36230],{"className":36229},[161,162,163,164],[60,36231,36233],{"className":36232},[127,164],[60,36234,820],{"className":36235},[127,164],[60,36237,213],{"className":36238},[212],[60,36240,36242],{"className":36241},[144],[60,36243,36245],{"className":36244,"style":3907},[148],[60,36246],{},[60,36248],{"className":36249},[267,132],"。\n所以 ",[26,36252,36253],{},[60,36254,36256,36315],{"className":36255},[63],[60,36257,36259],{"className":36258},[67],[69,36260,36261],{"xmlns":71},[73,36262,36263,36312],{},[76,36264,36265,36271,36273,36275,36277,36279,36303,36305,36308,36310],{},[96,36266,36267,36269],{},[84,36268,34591],{},[102,36270,820],{},[397,36272,400],{"stretchy":399},[84,36274,2152],{},[397,36276,405],{"stretchy":399},[397,36278,448],{},[79,36280,36281,36301],{},[76,36282,36283,36289,36291],{},[550,36284,36285,36287],{},[84,36286,981],{},[84,36288,2152],{},[397,36290,990],{},[550,36292,36293,36295],{},[84,36294,981],{},[76,36296,36297,36299],{},[397,36298,817],{},[84,36300,2152],{},[102,36302,814],{},[397,36304,448],{},[84,36306,36307],{},"cosh",[397,36309,1465],{},[84,36311,2152],{},[106,36313,36314],{"encoding":108},"\\phi_1(t) = \\frac{e^t + e^{-t}}{2} = \\cosh t",[60,36316,36318,36382,36531],{"className":36317,"ariaHidden":114},[113],[60,36319,36321,36324,36364,36367,36370,36373,36376,36379],{"className":36320},[118],[60,36322],{"className":36323,"style":418},[122],[60,36325,36327,36330],{"className":36326},[127],[60,36328,34591],{"className":36329},[127,178],[60,36331,36333],{"className":36332},[183],[60,36334,36336,36356],{"className":36335},[139,140],[60,36337,36339,36353],{"className":36338},[144],[60,36340,36342],{"className":36341,"style":318},[148],[60,36343,36344,36347],{"style":1940},[60,36345],{"className":36346,"style":325},[156],[60,36348,36350],{"className":36349},[161,162,163,164],[60,36351,820],{"className":36352},[127,164],[60,36354,213],{"className":36355},[212],[60,36357,36359],{"className":36358},[144],[60,36360,36362],{"className":36361,"style":341},[148],[60,36363],{},[60,36365,400],{"className":36366},[131],[60,36368,2152],{"className":36369},[127,178],[60,36371,405],{"className":36372},[267],[60,36374],{"className":36375,"style":470},[469],[60,36377,448],{"className":36378},[474],[60,36380],{"className":36381,"style":470},[469],[60,36383,36385,36389,36522,36525,36528],{"className":36384},[118],[60,36386],{"className":36387,"style":36388},[122],"height:1.3482em;vertical-align:-0.345em;",[60,36390,36392,36395,36519],{"className":36391},[127],[60,36393],{"className":36394},[131,132],[60,36396,36398],{"className":36397},[79],[60,36399,36401,36511],{"className":36400},[139,140],[60,36402,36404,36508],{"className":36403},[144],[60,36405,36408,36422,36430],{"className":36406,"style":36407},[148],"height:1.0032em;",[60,36409,36410,36413],{"style":152},[60,36411],{"className":36412,"style":157},[156],[60,36414,36416],{"className":36415},[161,162,163,164],[60,36417,36419],{"className":36418},[127,164],[60,36420,814],{"className":36421},[127,164],[60,36423,36424,36427],{"style":225},[60,36425],{"className":36426,"style":157},[156],[60,36428],{"className":36429,"style":233},[232],[60,36431,36432,36435],{"style":1105},[60,36433],{"className":36434,"style":157},[156],[60,36436,36438],{"className":36437},[161,162,163,164],[60,36439,36441,36470,36473],{"className":36440},[127,164],[60,36442,36444,36447],{"className":36443},[127,164],[60,36445,981],{"className":36446},[127,178,164],[60,36448,36450],{"className":36449},[183],[60,36451,36453],{"className":36452},[139],[60,36454,36456],{"className":36455},[144],[60,36457,36459],{"className":36458,"style":22945},[148],[60,36460,36461,36464],{"style":1142},[60,36462],{"className":36463,"style":200},[156],[60,36465,36467],{"className":36466},[161,204,205,164],[60,36468,2152],{"className":36469},[127,178,164],[60,36471,990],{"className":36472},[928,164],[60,36474,36476,36479],{"className":36475},[127,164],[60,36477,981],{"className":36478},[127,178,164],[60,36480,36482],{"className":36481},[183],[60,36483,36485],{"className":36484},[139],[60,36486,36488],{"className":36487},[144],[60,36489,36491],{"className":36490,"style":22945},[148],[60,36492,36493,36496],{"style":1142},[60,36494],{"className":36495,"style":200},[156],[60,36497,36499],{"className":36498},[161,204,205,164],[60,36500,36502,36505],{"className":36501},[127,164],[60,36503,817],{"className":36504},[127,164],[60,36506,2152],{"className":36507},[127,178,164],[60,36509,213],{"className":36510},[212],[60,36512,36514],{"className":36513},[144],[60,36515,36517],{"className":36516,"style":3907},[148],[60,36518],{},[60,36520],{"className":36521},[267,132],[60,36523],{"className":36524,"style":470},[469],[60,36526,448],{"className":36527},[474],[60,36529],{"className":36530,"style":470},[469],[60,36532,36534,36537,36540,36543],{"className":36533},[118],[60,36535],{"className":36536,"style":13418},[122],[60,36538,36307],{"className":36539},[1495],[60,36541],{"className":36542,"style":653},[469],[60,36544,2152],{"className":36545},[127,178]," (双曲余弦)。",[23,36548,36549,35263,36622,35555,36916,35943,37255,36250,37566,37859],{},[26,36550,36551,36552],{},"第二步：构造 ",[60,36553,36555,36573],{"className":36554},[63],[60,36556,36558],{"className":36557},[67],[69,36559,36560],{"xmlns":71},[73,36561,36562,36570],{},[76,36563,36564],{},[96,36565,36566,36568],{},[84,36567,34591],{},[102,36569,814],{},[106,36571,36572],{"encoding":108},"\\phi_2",[60,36574,36576],{"className":36575,"ariaHidden":114},[113],[60,36577,36579,36582],{"className":36578},[118],[60,36580],{"className":36581,"style":694},[122],[60,36583,36585,36588],{"className":36584},[127],[60,36586,34591],{"className":36587},[127,178],[60,36589,36591],{"className":36590},[183],[60,36592,36594,36614],{"className":36593},[139,140],[60,36595,36597,36611],{"className":36596},[144],[60,36598,36600],{"className":36599,"style":318},[148],[60,36601,36602,36605],{"style":1940},[60,36603],{"className":36604,"style":325},[156],[60,36606,36608],{"className":36607},[161,162,163,164],[60,36609,814],{"className":36610},[127,164],[60,36612,213],{"className":36613},[212],[60,36615,36617],{"className":36616},[144],[60,36618,36620],{"className":36619,"style":341},[148],[60,36621],{},[60,36623,36625,36682],{"className":36624},[63],[60,36626,36628],{"className":36627},[67],[69,36629,36630],{"xmlns":71},[73,36631,36632,36679],{},[76,36633,36634,36640,36642,36644,36646,36648,36655,36661,36663,36669],{},[96,36635,36636,36638],{},[84,36637,34591],{},[102,36639,814],{},[397,36641,400],{"stretchy":399},[84,36643,2152],{},[397,36645,405],{"stretchy":399},[397,36647,448],{},[96,36649,36650,36653],{},[84,36651,36652],{},"k",[102,36654,820],{},[550,36656,36657,36659],{},[84,36658,981],{},[84,36660,2152],{},[397,36662,990],{},[96,36664,36665,36667],{},[84,36666,36652],{},[102,36668,814],{},[550,36670,36671,36673],{},[84,36672,981],{},[76,36674,36675,36677],{},[397,36676,817],{},[84,36678,2152],{},[106,36680,36681],{"encoding":108},"\\phi_2(t) = k_1 e^t + k_2 e^{-t}",[60,36683,36685,36749,36835],{"className":36684,"ariaHidden":114},[113],[60,36686,36688,36691,36731,36734,36737,36740,36743,36746],{"className":36687},[118],[60,36689],{"className":36690,"style":418},[122],[60,36692,36694,36697],{"className":36693},[127],[60,36695,34591],{"className":36696},[127,178],[60,36698,36700],{"className":36699},[183],[60,36701,36703,36723],{"className":36702},[139,140],[60,36704,36706,36720],{"className":36705},[144],[60,36707,36709],{"className":36708,"style":318},[148],[60,36710,36711,36714],{"style":1940},[60,36712],{"className":36713,"style":325},[156],[60,36715,36717],{"className":36716},[161,162,163,164],[60,36718,814],{"className":36719},[127,164],[60,36721,213],{"className":36722},[212],[60,36724,36726],{"className":36725},[144],[60,36727,36729],{"className":36728,"style":341},[148],[60,36730],{},[60,36732,400],{"className":36733},[131],[60,36735,2152],{"className":36736},[127,178],[60,36738,405],{"className":36739},[267],[60,36741],{"className":36742,"style":470},[469],[60,36744,448],{"className":36745},[474],[60,36747],{"className":36748,"style":470},[469],[60,36750,36752,36755,36797,36826,36829,36832],{"className":36751},[118],[60,36753],{"className":36754,"style":24622},[122],[60,36756,36758,36762],{"className":36757},[127],[60,36759,36652],{"className":36760,"style":36761},[127,178],"margin-right:0.0315em;",[60,36763,36765],{"className":36764},[183],[60,36766,36768,36789],{"className":36767},[139,140],[60,36769,36771,36786],{"className":36770},[144],[60,36772,36774],{"className":36773,"style":318},[148],[60,36775,36777,36780],{"style":36776},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[60,36778],{"className":36779,"style":325},[156],[60,36781,36783],{"className":36782},[161,162,163,164],[60,36784,820],{"className":36785},[127,164],[60,36787,213],{"className":36788},[212],[60,36790,36792],{"className":36791},[144],[60,36793,36795],{"className":36794,"style":341},[148],[60,36796],{},[60,36798,36800,36803],{"className":36799},[127],[60,36801,981],{"className":36802},[127,178],[60,36804,36806],{"className":36805},[183],[60,36807,36809],{"className":36808},[139],[60,36810,36812],{"className":36811},[144],[60,36813,36815],{"className":36814,"style":20132},[148],[60,36816,36817,36820],{"style":608},[60,36818],{"className":36819,"style":325},[156],[60,36821,36823],{"className":36822},[161,162,163,164],[60,36824,2152],{"className":36825},[127,178,164],[60,36827],{"className":36828,"style":924},[469],[60,36830,990],{"className":36831},[928],[60,36833],{"className":36834,"style":924},[469],[60,36836,36838,36841,36881],{"className":36837},[118],[60,36839],{"className":36840,"style":24622},[122],[60,36842,36844,36847],{"className":36843},[127],[60,36845,36652],{"className":36846,"style":36761},[127,178],[60,36848,36850],{"className":36849},[183],[60,36851,36853,36873],{"className":36852},[139,140],[60,36854,36856,36870],{"className":36855},[144],[60,36857,36859],{"className":36858,"style":318},[148],[60,36860,36861,36864],{"style":36776},[60,36862],{"className":36863,"style":325},[156],[60,36865,36867],{"className":36866},[161,162,163,164],[60,36868,814],{"className":36869},[127,164],[60,36871,213],{"className":36872},[212],[60,36874,36876],{"className":36875},[144],[60,36877,36879],{"className":36878,"style":341},[148],[60,36880],{},[60,36882,36884,36887],{"className":36883},[127],[60,36885,981],{"className":36886},[127,178],[60,36888,36890],{"className":36889},[183],[60,36891,36893],{"className":36892},[139],[60,36894,36896],{"className":36895},[144],[60,36897,36899],{"className":36898,"style":20132},[148],[60,36900,36901,36904],{"style":608},[60,36902],{"className":36903,"style":325},[156],[60,36905,36907],{"className":36906},[161,162,163,164],[60,36908,36910,36913],{"className":36909},[127,164],[60,36911,817],{"className":36912},[127,164],[60,36914,2152],{"className":36915},[127,178,164],[60,36917,36919,36987],{"className":36918},[63],[60,36920,36922],{"className":36921},[67],[69,36923,36924],{"xmlns":71},[73,36925,36926,36984],{},[76,36927,36928,36930],{},[397,36929,20568],{"fence":114},[20570,36931,36932,36958],{"rowspacing":20572,"columnalign":20573,"columnspacing":13091},[20575,36933,36934],{},[20578,36935,36936],{},[20581,36937,36938],{"scriptlevel":104,"displaystyle":399},[76,36939,36940,36946,36948,36954,36956],{},[96,36941,36942,36944],{},[84,36943,36652],{},[102,36945,820],{},[397,36947,990],{},[96,36949,36950,36952],{},[84,36951,36652],{},[102,36953,814],{},[397,36955,448],{},[102,36957,104],{},[20575,36959,36960],{},[20578,36961,36962],{},[20581,36963,36964],{"scriptlevel":104,"displaystyle":399},[76,36965,36966,36972,36974,36980,36982],{},[96,36967,36968,36970],{},[84,36969,36652],{},[102,36971,820],{},[397,36973,817],{},[96,36975,36976,36978],{},[84,36977,36652],{},[102,36979,814],{},[397,36981,448],{},[102,36983,820],{},[106,36985,36986],{"encoding":108},"\\begin{cases}\nk_1 + k_2 = 0 \\\\\nk_1 - k_2 = 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= \\frac{e^t - e^{-t}}{2} = \\sinh t",[60,37631,37633,37697,37844],{"className":37632,"ariaHidden":114},[113],[60,37634,37636,37639,37679,37682,37685,37688,37691,37694],{"className":37635},[118],[60,37637],{"className":37638,"style":418},[122],[60,37640,37642,37645],{"className":37641},[127],[60,37643,34591],{"className":37644},[127,178],[60,37646,37648],{"className":37647},[183],[60,37649,37651,37671],{"className":37650},[139,140],[60,37652,37654,37668],{"className":37653},[144],[60,37655,37657],{"className":37656,"style":318},[148],[60,37658,37659,37662],{"style":1940},[60,37660],{"className":37661,"style":325},[156],[60,37663,37665],{"className":37664},[161,162,163,164],[60,37666,814],{"className":37667},[127,164],[60,37669,213],{"className":37670},[212],[60,37672,37674],{"className":37673},[144],[60,37675,37677],{"className":37676,"style":341},[148],[60,37678],{},[60,37680,400],{"className":37681},[131],[60,37683,2152],{"className":37684},[127,178],[60,37686,405],{"className":37687},[267],[60,37689],{"className":37690,"style":470},[469],[60,37692,448],{"className":37693},[474],[60,37695],{"className":37696,"style":470},[469],[60,37698,37700,37703,37835,37838,37841],{"className":37699},[118],[60,37701],{"className":37702,"style":36388},[122],[60,37704,37706,37709,37832],{"className":37705},[127],[60,37707],{"className":37708},[131,132],[60,37710,37712],{"className":37711},[79],[60,37713,37715,37824],{"className":37714},[139,140],[60,37716,37718,37821],{"className":37717},[144],[60,37719,37721,37735,37743],{"className":37720,"style":36407},[148],[60,37722,37723,37726],{"style":152},[60,37724],{"className":37725,"style":157},[156],[60,37727,37729],{"className":37728},[161,162,163,164],[60,37730,37732],{"className":37731},[127,164],[60,37733,814],{"className":37734},[127,164],[60,37736,37737,37740],{"style":225},[60,37738],{"className":37739,"style":157},[156],[60,37741],{"className":37742,"style":233},[232],[60,37744,37745,37748],{"style":1105},[60,37746],{"className":37747,"style":157},[156],[60,37749,37751],{"className":37750},[161,162,163,164],[60,37752,37754,37783,37786],{"className":37753},[127,164],[60,37755,37757,37760],{"className":37756},[127,164],[60,37758,981],{"className":37759},[127,178,164],[60,37761,37763],{"className":37762},[183],[60,37764,37766],{"className":37765},[139],[60,37767,37769],{"className":37768},[144],[60,37770,37772],{"className":37771,"style":22945},[148],[60,37773,37774,37777],{"style":1142},[60,37775],{"className":37776,"style":200},[156],[60,37778,37780],{"className":37779},[161,204,205,164],[60,37781,2152],{"className":37782},[127,178,164],[60,37784,817],{"className":37785},[928,164],[60,37787,37789,37792],{"className":37788},[127,164],[60,37790,981],{"className":37791},[127,178,164],[60,37793,37795],{"className":37794},[183],[60,37796,37798],{"className":37797},[139],[60,37799,37801],{"className":37800},[144],[60,37802,37804],{"className":37803,"style":22945},[148],[60,37805,37806,37809],{"style":1142},[60,37807],{"className":37808,"style":200},[156],[60,37810,37812],{"className":37811},[161,204,205,164],[60,37813,37815,37818],{"className":37814},[127,164],[60,37816,817],{"className":37817},[127,164],[60,37819,2152],{"className":37820},[127,178,164],[60,37822,213],{"className":37823},[212],[60,37825,37827],{"className":37826},[144],[60,37828,37830],{"className":37829,"style":3907},[148],[60,37831],{},[60,37833],{"className":37834},[267,132],[60,37836],{"className":37837,"style":470},[469],[60,37839,448],{"className":37840},[474],[60,37842],{"className":37843,"style":470},[469],[60,37845,37847,37850,37853,37856],{"className":37846},[118],[60,37848],{"className":37849,"style":13418},[122],[60,37851,37622],{"className":37852},[1495],[60,37854],{"className":37855,"style":653},[469],[60,37857,2152],{"className":37858},[127,178]," (双曲正弦)。",[23,37861,37862,37865,37866,38113,38114,38457],{},[26,37863,37864],{},"第三步：利用标准解组写任意解","\n有了这两个标准解，任意初值 ",[60,37867,37869,37921],{"className":37868},[63],[60,37870,37872],{"className":37871},[67],[69,37873,37874],{"xmlns":71},[73,37875,37876,37918],{},[76,37877,37878,37880,37882,37884,37886,37888,37894,37896,37902,37904,37906,37908,37910],{},[84,37879,359],{},[397,37881,400],{"stretchy":399},[102,37883,104],{},[397,37885,405],{"stretchy":399},[397,37887,448],{},[96,37889,37890,37892],{},[84,37891,359],{},[102,37893,104],{},[397,37895,569],{"separator":114},[550,37897,37898,37900],{},[84,37899,359],{},[397,37901,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,37903,400],{"stretchy":399},[102,37905,104],{},[397,37907,405],{"stretchy":399},[397,37909,448],{},[2127,37911,37912,37914,37916],{},[84,37913,359],{},[102,37915,104],{},[397,37917,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,37919,37920],{"encoding":108},"x(0)=x_0, x'(0)=x_0'",[60,37922,37924,37951,38053],{"className":37923,"ariaHidden":114},[113],[60,37925,37927,37930,37933,37936,37939,37942,37945,37948],{"className":37926},[118],[60,37928],{"className":37929,"style":418},[122],[60,37931,359],{"className":37932},[127,178],[60,37934,400],{"className":37935},[131],[60,37937,104],{"className":37938},[127],[60,37940,405],{"className":37941},[267],[60,37943],{"className":37944,"style":470},[469],[60,37946,448],{"className":37947},[474],[60,37949],{"className":37950,"style":470},[469],[60,37952,37954,37957,37997,38000,38003,38035,38038,38041,38044,38047,38050],{"className":37953},[118],[60,37955],{"className":37956,"style":10437},[122],[60,37958,37960,37963],{"className":37959},[127],[60,37961,359],{"className":37962},[127,178],[60,37964,37966],{"className":37965},[183],[60,37967,37969,37989],{"className":37968},[139,140],[60,37970,37972,37986],{"className":37971},[144],[60,37973,37975],{"className":37974,"style":318},[148],[60,37976,37977,37980],{"style":1940},[60,37978],{"className":37979,"style":325},[156],[60,37981,37983],{"className":37982},[161,162,163,164],[60,37984,104],{"className":37985},[127,164],[60,37987,213],{"className":37988},[212],[60,37990,37992],{"className":37991},[144],[60,37993,37995],{"className":37994,"style":341},[148],[60,37996],{},[60,37998,569],{"className":37999},[649],[60,38001],{"className":38002,"style":653},[469],[60,38004,38006,38009],{"className":38005},[127],[60,38007,359],{"className":38008},[127,178],[60,38010,38012],{"className":38011},[183],[60,38013,38015],{"className":38014},[139],[60,38016,38018],{"className":38017},[144],[60,38019,38021],{"className":38020,"style":605},[148],[60,38022,38023,38026],{"style":608},[60,38024],{"className":38025,"style":325},[156],[60,38027,38029],{"className":38028},[161,162,163,164],[60,38030,38032],{"className":38031},[127,164],[60,38033,557],{"className":38034},[127,164],[60,38036,400],{"className":38037},[131],[60,38039,104],{"className":38040},[127],[60,38042,405],{"className":38043},[267],[60,38045],{"className":38046,"style":470},[469],[60,38048,448],{"className":38049},[474],[60,38051],{"className":38052,"style":470},[469],[60,38054,38056,38059],{"className":38055},[118],[60,38057],{"className":38058,"style":17392},[122],[60,38060,38062,38065],{"className":38061},[127],[60,38063,359],{"className":38064},[127,178],[60,38066,38068],{"className":38067},[183],[60,38069,38071,38105],{"className":38070},[139,140],[60,38072,38074,38102],{"className":38073},[144],[60,38075,38077,38088],{"className":38076,"style":605},[148],[60,38078,38079,38082],{"style":17413},[60,38080],{"className":38081,"style":325},[156],[60,38083,38085],{"className":38084},[161,162,163,164],[60,38086,104],{"className":38087},[127,164],[60,38089,38090,38093],{"style":608},[60,38091],{"className":38092,"style":325},[156],[60,38094,38096],{"className":38095},[161,162,163,164],[60,38097,38099],{"className":38098},[127,164],[60,38100,557],{"className":38101},[127,164],[60,38103,213],{"className":38104},[212],[60,38106,38108],{"className":38107},[144],[60,38109,38111],{"className":38110,"style":17446},[148],[60,38112],{}," 的解直接写出来，不用计算：\n",[60,38115,38117,38183],{"className":38116},[63],[60,38118,38120],{"className":38119},[67],[69,38121,38122],{"xmlns":71},[73,38123,38124,38180],{},[76,38125,38126,38128,38130,38132,38134,38136,38142,38144,38150,38152,38154,38156,38158,38166,38168,38174,38176,38178],{},[84,38127,359],{},[397,38129,400],{"stretchy":399},[84,38131,2152],{},[397,38133,405],{"stretchy":399},[397,38135,448],{},[96,38137,38138,38140],{},[84,38139,359],{},[102,38141,104],{},[397,38143,2831],{},[96,38145,38146,38148],{},[84,38147,34591],{},[102,38149,820],{},[397,38151,400],{"stretchy":399},[84,38153,2152],{},[397,38155,405],{"stretchy":399},[397,38157,990],{},[2127,38159,38160,38162,38164],{},[84,38161,359],{},[102,38163,104],{},[397,38165,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,38167,2831],{},[96,38169,38170,38172],{},[84,38171,34591],{},[102,38173,814],{},[397,38175,400],{"stretchy":399},[84,38177,2152],{},[397,38179,405],{"stretchy":399},[106,38181,38182],{"encoding":108},"x(t) = x_0 \\cdot \\phi_1(t) + x_0' \\cdot \\phi_2(t)",[60,38184,38186,38213,38269,38333,38402],{"className":38185,"ariaHidden":114},[113],[60,38187,38189,38192,38195,38198,38201,38204,38207,38210],{"className":38188},[118],[60,38190],{"className":38191,"style":418},[122],[60,38193,359],{"className":38194},[127,178],[60,38196,400],{"className":38197},[131],[60,38199,2152],{"className":38200},[127,178],[60,38202,405],{"className":38203},[267],[60,38205],{"className":38206,"style":470},[469],[60,38208,448],{"className":38209},[474],[60,38211],{"className":38212,"style":470},[469],[60,38214,38216,38220,38260,38263,38266],{"className":38215},[118],[60,38217],{"className":38218,"style":38219},[122],"height:0.5945em;vertical-align:-0.15em;",[60,38221,38223,38226],{"className":38222},[127],[60,38224,359],{"className":38225},[127,178],[60,38227,38229],{"className":38228},[183],[60,38230,38232,38252],{"className":38231},[139,140],[60,38233,38235,38249],{"className":38234},[144],[60,38236,38238],{"className":38237,"style":318},[148],[60,38239,38240,38243],{"style":1940},[60,38241],{"className":38242,"style":325},[156],[60,38244,38246],{"className":38245},[161,162,163,164],[60,38247,104],{"className":38248},[127,164],[60,38250,213],{"className":38251},[212],[60,38253,38255],{"className":38254},[144],[60,38256,38258],{"className":38257,"style":341},[148],[60,38259],{},[60,38261],{"className":38262,"style":924},[469],[60,38264,2831],{"className":38265},[928],[60,38267],{"className":38268,"style":924},[469],[60,38270,38272,38275,38315,38318,38321,38324,38327,38330],{"className":38271},[118],[60,38273],{"className":38274,"style":418},[122],[60,38276,38278,38281],{"className":38277},[127],[60,38279,34591],{"className":38280},[127,178],[60,38282,38284],{"className":38283},[183],[60,38285,38287,38307],{"className":38286},[139,140],[60,38288,38290,38304],{"className":38289},[144],[60,38291,38293],{"className":38292,"style":318},[148],[60,38294,38295,38298],{"style":1940},[60,38296],{"className":38297,"style":325},[156],[60,38299,38301],{"className":38300},[161,162,163,164],[60,38302,820],{"className":38303},[127,164],[60,38305,213],{"className":38306},[212],[60,38308,38310],{"className":38309},[144],[60,38311,38313],{"className":38312,"style":341},[148],[60,38314],{},[60,38316,400],{"className":38317},[131],[60,38319,2152],{"className":38320},[127,178],[60,38322,405],{"className":38323},[267],[60,38325],{"className":38326,"style":924},[469],[60,38328,990],{"className":38329},[928],[60,38331],{"className":38332,"style":924},[469],[60,38334,38336,38339,38393,38396,38399],{"className":38335},[118],[60,38337],{"className":38338,"style":17392},[122],[60,38340,38342,38345],{"className":38341},[127],[60,38343,359],{"className":38344},[127,178],[60,38346,38348],{"className":38347},[183],[60,38349,38351,38385],{"className":38350},[139,140],[60,38352,38354,38382],{"className":38353},[144],[60,38355,38357,38368],{"className":38356,"style":605},[148],[60,38358,38359,38362],{"style":17413},[60,38360],{"className":38361,"style":325},[156],[60,38363,38365],{"className":38364},[161,162,163,164],[60,38366,104],{"className":38367},[127,164],[60,38369,38370,38373],{"style":608},[60,38371],{"className":38372,"style":325},[156],[60,38374,38376],{"className":38375},[161,162,163,164],[60,38377,38379],{"className":38378},[127,164],[60,38380,557],{"className":38381},[127,164],[60,38383,213],{"className":38384},[212],[60,38386,38388],{"className":38387},[144],[60,38389,38391],{"className":38390,"style":17446},[148],[60,38392],{},[60,38394],{"className":38395,"style":924},[469],[60,38397,2831],{"className":38398},[928],[60,38400],{"className":38401,"style":924},[469],[60,38403,38405,38408,38448,38451,38454],{"className":38404},[118],[60,38406],{"className":38407,"style":418},[122],[60,38409,38411,38414],{"className":38410},[127],[60,38412,34591],{"className":38413},[127,178],[60,38415,38417],{"className":38416},[183],[60,38418,38420,38440],{"className":38419},[139,140],[60,38421,38423,38437],{"className":38422},[144],[60,38424,38426],{"className":38425,"style":318},[148],[60,38427,38428,38431],{"style":1940},[60,38429],{"className":38430,"style":325},[156],[60,38432,38434],{"className":38433},[161,162,163,164],[60,38435,814],{"className":38436},[127,164],[60,38438,213],{"className":38439},[212],[60,38441,38443],{"className":38442},[144],[60,38444,38446],{"className":38445,"style":341},[148],[60,38447],{},[60,38449,400],{"className":38450},[131],[60,38452,2152],{"className":38453},[127,178],[60,38455,405],{"className":38456},[267],[60,38458,38460,38510],{"className":38459},[63],[60,38461,38463],{"className":38462},[67],[69,38464,38465],{"xmlns":71},[73,38466,38467,38507],{},[76,38468,38469,38471,38473,38475,38477,38479,38485,38487,38489,38491,38493,38501,38503,38505],{},[84,38470,359],{},[397,38472,400],{"stretchy":399},[84,38474,2152],{},[397,38476,405],{"stretchy":399},[397,38478,448],{},[96,38480,38481,38483],{},[84,38482,359],{},[102,38484,104],{},[84,38486,36307],{},[397,38488,1465],{},[84,38490,2152],{},[397,38492,990],{},[2127,38494,38495,38497,38499],{},[84,38496,359],{},[102,38498,104],{},[397,38500,557],{"mathvariant":86,"lspace":556,"rspace":556},[84,38502,37622],{},[397,38504,1465],{},[84,38506,2152],{},[106,38508,38509],{"encoding":108},"x(t) = x_0 \\cosh t + x_0' \\sinh t",[60,38511,38513,38540,38607],{"className":38512,"ariaHidden":114},[113],[60,38514,38516,38519,38522,38525,38528,38531,38534,38537],{"className":38515},[118],[60,38517],{"className":38518,"style":418},[122],[60,38520,359],{"className":38521},[127,178],[60,38523,400],{"className":38524},[131],[60,38526,2152],{"className":38527},[127,178],[60,38529,405],{"className":38530},[267],[60,38532],{"className":38533,"style":470},[469],[60,38535,448],{"className":38536},[474],[60,38538],{"className":38539,"style":470},[469],[60,38541,38543,38546,38586,38589,38592,38595,38598,38601,38604],{"className":38542},[118],[60,38544],{"className":38545,"style":34342},[122],[60,38547,38549,38552],{"className":38548},[127],[60,38550,359],{"className":38551},[127,178],[60,38553,38555],{"className":38554},[183],[60,38556,38558,38578],{"className":38557},[139,140],[60,38559,38561,38575],{"className":38560},[144],[60,38562,38564],{"className":38563,"style":318},[148],[60,38565,38566,38569],{"style":1940},[60,38567],{"className":38568,"style":325},[156],[60,38570,38572],{"className":38571},[161,162,163,164],[60,38573,104],{"className":38574},[127,164],[60,38576,213],{"className":38577},[212],[60,38579,38581],{"className":38580},[144],[60,38582,38584],{"className":38583,"style":341},[148],[60,38585],{},[60,38587],{"className":38588,"style":653},[469],[60,38590,36307],{"className":38591},[1495],[60,38593],{"className":38594,"style":653},[469],[60,38596,2152],{"className":38597},[127,178],[60,38599],{"className":38600,"style":924},[469],[60,38602,990],{"className":38603},[928],[60,38605],{"className":38606,"style":924},[469],[60,38608,38610,38613,38667,38670,38673,38676],{"className":38609},[118],[60,38611],{"className":38612,"style":17392},[122],[60,38614,38616,38619],{"className":38615},[127],[60,38617,359],{"className":38618},[127,178],[60,38620,38622],{"className":38621},[183],[60,38623,38625,38659],{"className":38624},[139,140],[60,38626,38628,38656],{"className":38627},[144],[60,38629,38631,38642],{"className":38630,"style":605},[148],[60,38632,38633,38636],{"style":17413},[60,38634],{"className":38635,"style":325},[156],[60,38637,38639],{"className":38638},[161,162,163,164],[60,38640,104],{"className":38641},[127,164],[60,38643,38644,38647],{"style":608},[60,38645],{"className":38646,"style":325},[156],[60,38648,38650],{"className":38649},[161,162,163,164],[60,38651,38653],{"className":38652},[127,164],[60,38654,557],{"className":38655},[127,164],[60,38657,213],{"className":38658},[212],[60,38660,38662],{"className":38661},[144],[60,38663,38665],{"className":38664,"style":17446},[148],[60,38666],{},[60,38668],{"className":38669,"style":653},[469],[60,38671,37622],{"className":38672},[1495],[60,38674],{"className":38675,"style":653},[469],[60,38677,2152],{"className":38678},[127,178],[15,38680],{},[18,38682,38684],{"id":38683},"_5-朗斯基行列式的导数刘维尔公式","5. 朗斯基行列式的导数（刘维尔公式）",[23,38686,38687,38688,488],{},"这是一个理论证明题，核心在于",[26,38689,38690],{},"行列式怎么求导",[23,38692,38693,38696,38697],{},[26,38694,38695],{},"证明思路：","\n行列式求导法则：",[26,38698,38699],{},"等于“每次只对一行求导，其他行不变”的行列式之和。",[23,38701,38702,38703,38731,38732,15718],{},"对于 ",[60,38704,38706,38719],{"className":38705},[63],[60,38707,38709],{"className":38708},[67],[69,38710,38711],{"xmlns":71},[73,38712,38713,38717],{},[76,38714,38715],{},[84,38716,16342],{},[106,38718,16342],{"encoding":108},[60,38720,38722],{"className":38721,"ariaHidden":114},[113],[60,38723,38725,38728],{"className":38724},[118],[60,38726],{"className":38727,"style":371},[122],[60,38729,16342],{"className":38730},[127,178]," 阶朗斯基行列式 ",[60,38733,38735,38756],{"className":38734},[63],[60,38736,38738],{"className":38737},[67],[69,38739,38740],{"xmlns":71},[73,38741,38742,38753],{},[76,38743,38744,38747,38749,38751],{},[84,38745,38746],{},"W",[397,38748,400],{"stretchy":399},[84,38750,2152],{},[397,38752,405],{"stretchy":399},[106,38754,38755],{"encoding":108},"W(t)",[60,38757,38759],{"className":38758,"ariaHidden":114},[113],[60,38760,38762,38765,38768,38771,38774],{"className":38761},[118],[60,38763],{"className":38764,"style":418},[122],[60,38766,38746],{"className":38767,"style":3572},[127,178],[60,38769,400],{"className":38770},[131],[60,38772,2152],{"className":38773},[127,178],[60,38775,405],{"className":38776},[267],[30,38778,38779,39057,39133,39283,40193,40962,41310,41432],{},[33,38780,38781,38782,38853,38854,38943,38944,488],{},"第一行是 ",[60,38783,38785,38803],{"className":38784},[63],[60,38786,38788],{"className":38787},[67],[69,38789,38790],{"xmlns":71},[73,38791,38792,38800],{},[76,38793,38794],{},[96,38795,38796,38798],{},[84,38797,359],{},[84,38799,23005],{},[106,38801,38802],{"encoding":108},"x_i",[60,38804,38806],{"className":38805,"ariaHidden":114},[113],[60,38807,38809,38812],{"className":38808},[118],[60,38810],{"className":38811,"style":2734},[122],[60,38813,38815,38818],{"className":38814},[127],[60,38816,359],{"className":38817},[127,178],[60,38819,38821],{"className":38820},[183],[60,38822,38824,38845],{"className":38823},[139,140],[60,38825,38827,38842],{"className":38826},[144],[60,38828,38831],{"className":38829,"style":38830},[148],"height:0.3117em;",[60,38832,38833,38836],{"style":1940},[60,38834],{"className":38835,"style":325},[156],[60,38837,38839],{"className":38838},[161,162,163,164],[60,38840,23005],{"className":38841},[127,178,164],[60,38843,213],{"className":38844},[212],[60,38846,38848],{"className":38847},[144],[60,38849,38851],{"className":38850,"style":341},[148],[60,38852],{},"，第二行是 ",[60,38855,38857,38877],{"className":38856},[63],[60,38858,38860],{"className":38859},[67],[69,38861,38862],{"xmlns":71},[73,38863,38864,38874],{},[76,38865,38866],{},[2127,38867,38868,38870,38872],{},[84,38869,359],{},[84,38871,23005],{},[397,38873,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,38875,38876],{"encoding":108},"x_i'",[60,38878,38880],{"className":38879,"ariaHidden":114},[113],[60,38881,38883,38887],{"className":38882},[118],[60,38884],{"className":38885,"style":38886},[122],"height:1.0106em;vertical-align:-0.2587em;",[60,38888,38890,38893],{"className":38889},[127],[60,38891,359],{"className":38892},[127,178],[60,38894,38896],{"className":38895},[183],[60,38897,38899,38934],{"className":38898},[139,140],[60,38900,38902,38931],{"className":38901},[144],[60,38903,38905,38917],{"className":38904,"style":605},[148],[60,38906,38908,38911],{"style":38907},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[60,38909],{"className":38910,"style":325},[156],[60,38912,38914],{"className":38913},[161,162,163,164],[60,38915,23005],{"className":38916},[127,178,164],[60,38918,38919,38922],{"style":608},[60,38920],{"className":38921,"style":325},[156],[60,38923,38925],{"className":38924},[161,162,163,164],[60,38926,38928],{"className":38927},[127,164],[60,38929,557],{"className":38930},[127,164],[60,38932,213],{"className":38933},[212],[60,38935,38937],{"className":38936},[144],[60,38938,38941],{"className":38939,"style":38940},[148],"height:0.2587em;",[60,38942],{},"，……，最后一行是 ",[60,38945,38947,38977],{"className":38946},[63],[60,38948,38950],{"className":38949},[67],[69,38951,38952],{"xmlns":71},[73,38953,38954,38974],{},[76,38955,38956],{},[2127,38957,38958,38960,38962],{},[84,38959,359],{},[84,38961,23005],{},[76,38963,38964,38966,38968,38970,38972],{},[397,38965,400],{"stretchy":399},[84,38967,16342],{},[397,38969,817],{},[102,38971,820],{},[397,38973,405],{"stretchy":399},[106,38975,38976],{"encoding":108},"x_i^{(n-1)}",[60,38978,38980],{"className":38979,"ariaHidden":114},[113],[60,38981,38983,38987],{"className":38982},[118],[60,38984],{"className":38985,"style":38986},[122],"height:1.3217em;vertical-align:-0.2769em;",[60,38988,38990,38993],{"className":38989},[127],[60,38991,359],{"className":38992},[127,178],[60,38994,38996],{"className":38995},[183],[60,38997,38999,39048],{"className":38998},[139,140],[60,39000,39002,39045],{"className":39001},[144],[60,39003,39006,39018],{"className":39004,"style":39005},[148],"height:1.0448em;",[60,39007,39009,39012],{"style":39008},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[60,39010],{"className":39011,"style":325},[156],[60,39013,39015],{"className":39014},[161,162,163,164],[60,39016,23005],{"className":39017},[127,178,164],[60,39019,39021,39024],{"style":39020},"top:-3.2198em;margin-right:0.05em;",[60,39022],{"className":39023,"style":325},[156],[60,39025,39027],{"className":39026},[161,162,163,164],[60,39028,39030,39033,39036,39039,39042],{"className":39029},[127,164],[60,39031,400],{"className":39032},[131,164],[60,39034,16342],{"className":39035},[127,178,164],[60,39037,817],{"className":39038},[928,164],[60,39040,820],{"className":39041},[127,164],[60,39043,405],{"className":39044},[267,164],[60,39046,213],{"className":39047},[212],[60,39049,39051],{"className":39050},[144],[60,39052,39055],{"className":39053,"style":39054},[148],"height:0.2769em;",[60,39056],{},[33,39058,39059,39060,39103,39104,39132],{},"对 ",[60,39061,39063,39082],{"className":39062},[63],[60,39064,39066],{"className":39065},[67],[69,39067,39068],{"xmlns":71},[73,39069,39070,39080],{},[76,39071,39072,39074,39076,39078],{},[84,39073,38746],{},[397,39075,400],{"stretchy":399},[84,39077,2152],{},[397,39079,405],{"stretchy":399},[106,39081,38755],{"encoding":108},[60,39083,39085],{"className":39084,"ariaHidden":114},[113],[60,39086,39088,39091,39094,39097,39100],{"className":39087},[118],[60,39089],{"className":39090,"style":418},[122],[60,39092,38746],{"className":39093,"style":3572},[127,178],[60,39095,400],{"className":39096},[131],[60,39098,2152],{"className":39099},[127,178],[60,39101,405],{"className":39102},[267]," 求导，会得到 ",[60,39105,39107,39120],{"className":39106},[63],[60,39108,39110],{"className":39109},[67],[69,39111,39112],{"xmlns":71},[73,39113,39114,39118],{},[76,39115,39116],{},[84,39117,16342],{},[106,39119,16342],{"encoding":108},[60,39121,39123],{"className":39122,"ariaHidden":114},[113],[60,39124,39126,39129],{"className":39125},[118],[60,39127],{"className":39128,"style":371},[122],[60,39130,16342],{"className":39131},[127,178]," 个行列式的和。",[33,39134,39135,39138,39139,39190,39191,39194,39195,39280,39281,488],{},[26,39136,39137],{},"关键点","：前 ",[60,39140,39142,39160],{"className":39141},[63],[60,39143,39145],{"className":39144},[67],[69,39146,39147],{"xmlns":71},[73,39148,39149,39157],{},[76,39150,39151,39153,39155],{},[84,39152,16342],{},[397,39154,817],{},[102,39156,820],{},[106,39158,39159],{"encoding":108},"n-1",[60,39161,39163,39181],{"className":39162,"ariaHidden":114},[113],[60,39164,39166,39169,39172,39175,39178],{"className":39165},[118],[60,39167],{"className":39168,"style":17099},[122],[60,39170,16342],{"className":39171},[127,178],[60,39173],{"className":39174,"style":924},[469],[60,39176,817],{"className":39177},[928],[60,39179],{"className":39180,"style":924},[469],[60,39182,39184,39187],{"className":39183},[118],[60,39185],{"className":39186,"style":484},[122],[60,39188,820],{"className":39189},[127]," 个行列式中，都会出现",[26,39192,39193],{},"两行完全一样","的情况（比如对第一行求导变成 ",[60,39196,39198,39217],{"className":39197},[63],[60,39199,39201],{"className":39200},[67],[69,39202,39203],{"xmlns":71},[73,39204,39205,39215],{},[76,39206,39207],{},[2127,39208,39209,39211,39213],{},[84,39210,359],{},[84,39212,23005],{},[397,39214,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,39216,38876],{"encoding":108},[60,39218,39220],{"className":39219,"ariaHidden":114},[113],[60,39221,39223,39226],{"className":39222},[118],[60,39224],{"className":39225,"style":38886},[122],[60,39227,39229,39232],{"className":39228},[127],[60,39230,359],{"className":39231},[127,178],[60,39233,39235],{"className":39234},[183],[60,39236,39238,39272],{"className":39237},[139,140],[60,39239,39241,39269],{"className":39240},[144],[60,39242,39244,39255],{"className":39243,"style":605},[148],[60,39245,39246,39249],{"style":38907},[60,39247],{"className":39248,"style":325},[156],[60,39250,39252],{"className":39251},[161,162,163,164],[60,39253,23005],{"className":39254},[127,178,164],[60,39256,39257,39260],{"style":608},[60,39258],{"className":39259,"style":325},[156],[60,39261,39263],{"className":39262},[161,162,163,164],[60,39264,39266],{"className":39265},[127,164],[60,39267,557],{"className":39268},[127,164],[60,39270,213],{"className":39271},[212],[60,39273,39275],{"className":39274},[144],[60,39276,39278],{"className":39277,"style":38940},[148],[60,39279],{},"，这就和原来的第二行一样了）。两行一样的行列式等于 ",[26,39282,104],{},[33,39284,39285,39288,39289,39292,39293,21834],{},[26,39286,39287],{},"唯一剩下的","：只有对",[26,39290,39291],{},"最后一行","求导的那个行列式不为0。\n[\n",[60,39294,39296,39486],{"className":39295},[63],[60,39297,39299],{"className":39298},[67],[69,39300,39301],{"xmlns":71},[73,39302,39303,39483],{},[76,39304,39305,39311,39313],{},[550,39306,39307,39309],{},[84,39308,38746],{},[397,39310,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,39312,448],{},[76,39314,39315,39317,39481],{},[397,39316,11774],{"fence":114},[20570,39318,39321,39349,39385,39437],{"rowspacing":39319,"columnalign":39320,"columnspacing":13091},"0.16em","center center center",[20575,39322,39323,39333,39339],{},[20578,39324,39325],{},[20581,39326,39327],{"scriptlevel":104,"displaystyle":399},[96,39328,39329,39331],{},[84,39330,359],{},[102,39332,820],{},[20578,39334,39335],{},[20581,39336,39337],{"scriptlevel":104,"displaystyle":399},[397,39338,16359],{"lspace":556,"rspace":556},[20578,39340,39341],{},[20581,39342,39343],{"scriptlevel":104,"displaystyle":399},[96,39344,39345,39347],{},[84,39346,359],{},[84,39348,16342],{},[20575,39350,39351,39367,39373],{},[20578,39352,39353],{},[20581,39354,39355],{"scriptlevel":104,"displaystyle":399},[76,39356,39357,39360],{},[84,39358,39359],{"mathvariant":86},"⋮",[39361,39362,39363],"mpadded",{"height":556,"voffset":556},[469,39364],{"mathbackground":39365,"width":556,"height":39366},"black","1.5em",[20578,39368,39369],{},[20581,39370,39371],{"scriptlevel":104,"displaystyle":399},[76,39372],{},[20578,39374,39375],{},[20581,39376,39377],{"scriptlevel":104,"displaystyle":399},[76,39378,39379,39381],{},[84,39380,39359],{"mathvariant":86},[39361,39382,39383],{"height":556,"voffset":556},[469,39384],{"mathbackground":39365,"width":556,"height":39366},[20575,39386,39387,39409,39415],{},[20578,39388,39389],{},[20581,39390,39391],{"scriptlevel":104,"displaystyle":399},[2127,39392,39393,39395,39397],{},[84,39394,359],{},[102,39396,820],{},[76,39398,39399,39401,39403,39405,39407],{},[397,39400,400],{"stretchy":399},[84,39402,16342],{},[397,39404,817],{},[102,39406,814],{},[397,39408,405],{"stretchy":399},[20578,39410,39411],{},[20581,39412,39413],{"scriptlevel":104,"displaystyle":399},[397,39414,16359],{"lspace":556,"rspace":556},[20578,39416,39417],{},[20581,39418,39419],{"scriptlevel":104,"displaystyle":399},[2127,39420,39421,39423,39425],{},[84,39422,359],{},[84,39424,16342],{},[76,39426,39427,39429,39431,39433,39435],{},[397,39428,400],{"stretchy":399},[84,39430,16342],{},[397,39432,817],{},[102,39434,814],{},[397,39436,405],{"stretchy":399},[20575,39438,39439,39457,39463],{},[20578,39440,39441],{},[20581,39442,39443],{"scriptlevel":104,"displaystyle":399},[2127,39444,39445,39447,39449],{},[84,39446,359],{"mathvariant":6025},[102,39448,820],{"mathvariant":6025},[76,39450,39451,39453,39455],{},[397,39452,400],{"stretchy":399},[84,39454,16342],{"mathvariant":6025},[397,39456,405],{"stretchy":399},[20578,39458,39459],{},[20581,39460,39461],{"scriptlevel":104,"displaystyle":399},[397,39462,16359],{"lspace":556,"rspace":556},[20578,39464,39465],{},[20581,39466,39467],{"scriptlevel":104,"displaystyle":399},[2127,39468,39469,39471,39473],{},[84,39470,359],{"mathvariant":6025},[84,39472,16342],{"mathvariant":6025},[76,39474,39475,39477,39479],{},[397,39476,400],{"stretchy":399},[84,39478,16342],{"mathvariant":6025},[397,39480,405],{"stretchy":399},[397,39482,11774],{"fence":114},[106,39484,39485],{"encoding":108},"W' = \\begin{vmatrix} x_1 & \\cdots & x_n \\\\ \\vdots & & \\vdots \\\\ x_1^{(n-2)} & \\cdots & x_n^{(n-2)} \\\\ \\mathbf{x_1^{(n)}} & \\cdots & \\mathbf{x_n^{(n)}} \\end{vmatrix}",[60,39487,39489,39536],{"className":39488,"ariaHidden":114},[113],[60,39490,39492,39495,39527,39530,39533],{"className":39491},[118],[60,39493],{"className":39494,"style":605},[122],[60,39496,39498,39501],{"className":39497},[127],[60,39499,38746],{"className":39500,"style":3572},[127,178],[60,39502,39504],{"className":39503},[183],[60,39505,39507],{"className":39506},[139],[60,39508,39510],{"className":39509},[144],[60,39511,39513],{"className":39512,"style":605},[148],[60,39514,39515,39518],{"style":608},[60,39516],{"className":39517,"style":325},[156],[60,39519,39521],{"className":39520},[161,162,163,164],[60,39522,39524],{"className":39523},[127,164],[60,39525,557],{"className":39526},[127,164],[60,39528],{"className":39529,"style":470},[469],[60,39531,448],{"className":39532},[474],[60,39534],{"className":39535,"style":470},[469],[60,39537,39539,39543],{"className":39538},[118],[60,39540],{"className":39541,"style":39542},[122],"height:5.8696em;vertical-align:-2.6848em;",[60,39544,39546,39591,40156],{"className":39545},[2326],[60,39547,39549],{"className":39548},[131],[60,39550,39552],{"className":39551},[2335,11923],[60,39553,39555,39582],{"className":39554},[139,140],[60,39556,39558,39579],{"className":39557},[144],[60,39559,39562],{"className":39560,"style":39561},[148],"height:2.95em;",[60,39563,39565,39569],{"style":39564},"top:-4.95em;",[60,39566],{"className":39567,"style":39568},[156],"height:7.4em;",[60,39570,39572],{"style":39571},"width:0.333em;height:5.4em;",[11945,39573,39576],{"xmlns":11947,"width":11948,"height":39574,"viewBox":39575},"5.4em","0 0 333 5400",[11952,39577],{"d":39578},"M145 15 v585 v4200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-4200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v4200 v585 h43z",[60,39580,213],{"className":39581},[212],[60,39583,39585],{"className":39584},[144],[60,39586,39589],{"className":39587,"style":39588},[148],"height:2.45em;",[60,39590],{},[60,39592,39594],{"className":39593},[127],[60,39595,39597,39839,39844,39847,39916,39919,39922],{"className":39596},[20570],[60,39598,39601],{"className":39599},[39600],"col-align-c",[60,39602,39604,39830],{"className":39603},[139,140],[60,39605,39607,39827],{"className":39606},[144],[60,39608,39611,39661,39681,39758],{"className":39609,"style":39610},[148],"height:3.1848em;",[60,39612,39614,39618],{"style":39613},"top:-6.0323em;",[60,39615],{"className":39616,"style":39617},[156],"height:3.6875em;",[60,39619,39621],{"className":39620},[127],[60,39622,39624,39627],{"className":39623},[127],[60,39625,359],{"className":39626},[127,178],[60,39628,39630],{"className":39629},[183],[60,39631,39633,39653],{"className":39632},[139,140],[60,39634,39636,39650],{"className":39635},[144],[60,39637,39639],{"className":39638,"style":318},[148],[60,39640,39641,39644],{"style":1940},[60,39642],{"className":39643,"style":325},[156],[60,39645,39647],{"className":39646},[161,162,163,164],[60,39648,820],{"className":39649},[127,164],[60,39651,213],{"className":39652},[212],[60,39654,39656],{"className":39655},[144],[60,39657,39659],{"className":39658,"style":341},[148],[60,39660],{},[60,39662,39664,39667],{"style":39663},"top:-4.1723em;",[60,39665],{"className":39666,"style":39617},[156],[60,39668,39670],{"className":39669},[127],[60,39671,39673,39676],{"className":39672},[127],[60,39674,39359],{"className":39675},[127],[60,39677],{"className":39678,"style":39680},[127,39679],"katex-rule","border-right-width:0em;border-top-width:1.5em;bottom:0em;",[60,39682,39684,39687],{"style":39683},"top:-2.7675em;",[60,39685],{"className":39686,"style":39617},[156],[60,39688,39690],{"className":39689},[127],[60,39691,39693,39696],{"className":39692},[127],[60,39694,359],{"className":39695},[127,178],[60,39697,39699],{"className":39698},[183],[60,39700,39702,39749],{"className":39701},[139,140],[60,39703,39705,39746],{"className":39704},[144],[60,39706,39708,39720],{"className":39707,"style":39005},[148],[60,39709,39711,39714],{"style":39710},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[60,39712],{"className":39713,"style":325},[156],[60,39715,39717],{"className":39716},[161,162,163,164],[60,39718,820],{"className":39719},[127,164],[60,39721,39722,39725],{"style":39020},[60,39723],{"className":39724,"style":325},[156],[60,39726,39728],{"className":39727},[161,162,163,164],[60,39729,39731,39734,39737,39740,39743],{"className":39730},[127,164],[60,39732,400],{"className":39733},[131,164],[60,39735,16342],{"className":39736},[127,178,164],[60,39738,817],{"className":39739},[928,164],[60,39741,814],{"className":39742},[127,164],[60,39744,405],{"className":39745},[267,164],[60,39747,213],{"className":39748},[212],[60,39750,39752],{"className":39751},[144],[60,39753,39756],{"className":39754,"style":39755},[148],"height:0.2663em;",[60,39757],{},[60,39759,39761,39764],{"style":39760},"top:-1.3627em;",[60,39762],{"className":39763,"style":39617},[156],[60,39765,39767],{"className":39766},[127],[60,39768,39770,39773],{"className":39769},[127],[60,39771,359],{"className":39772},[127,6121],[60,39774,39776],{"className":39775},[183],[60,39777,39779,39819],{"className":39778},[139,140],[60,39780,39782,39816],{"className":39781},[144],[60,39783,39785,39796],{"className":39784,"style":39005},[148],[60,39786,39787,39790],{"style":39710},[60,39788],{"className":39789,"style":325},[156],[60,39791,39793],{"className":39792},[161,162,163,164],[60,39794,820],{"className":39795},[127,6121,164],[60,39797,39798,39801],{"style":39020},[60,39799],{"className":39800,"style":325},[156],[60,39802,39804],{"className":39803},[161,162,163,164],[60,39805,39807,39810,39813],{"className":39806},[127,164],[60,39808,400],{"className":39809},[131,164],[60,39811,16342],{"className":39812},[127,6121,164],[60,39814,405],{"className":39815},[267,164],[60,39817,213],{"className":39818},[212],[60,39820,39822],{"className":39821},[144],[60,39823,39825],{"className":39824,"style":39755},[148],[60,39826],{},[60,39828,213],{"className":39829},[212],[60,39831,39833],{"className":39832},[144],[60,39834,39837],{"className":39835,"style":39836},[148],"height:2.6848em;",[60,39838],{},[60,39840],{"className":39841,"style":39843},[39842],"arraycolsep","width:0.5em;",[60,39845],{"className":39846,"style":39843},[39842],[60,39848,39850],{"className":39849},[39600],[60,39851,39853,39908],{"className":39852},[139,140],[60,39854,39856,39905],{"className":39855},[144],[60,39857,39859,39872,39881,39893],{"className":39858,"style":39610},[148],[60,39860,39862,39866],{"style":39861},"top:-5.8448em;",[60,39863],{"className":39864,"style":39865},[156],"height:3.5em;",[60,39867,39869],{"className":39868},[127],[60,39870,16359],{"className":39871},[2326],[60,39873,39875,39878],{"style":39874},"top:-3.9848em;",[60,39876],{"c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",[60,40200,40202,40219],{"className":40201},[63],[60,40203,40205],{"className":40204},[67],[69,40206,40207],{"xmlns":71},[73,40208,40209,40217],{},[76,40210,40211],{},[96,40212,40213,40215],{},[84,40214,359],{},[84,40216,23005],{},[106,40218,38802],{"encoding":108},[60,40220,40222],{"className":40221,"ariaHidden":114},[113],[60,40223,40225,40228],{"className":40224},[118],[60,40226],{"className":40227,"style":2734},[122],[60,40229,40231,40234],{"className":40230},[127],[60,40232,359],{"className":40233},[127,178],[60,40235,40237],{"className":40236},[183],[60,40238,40240,40260],{"className":40239},[139,140],[60,40241,40243,40257],{"className":40242},[144],[60,40244,40246],{"className":40245,"style":38830},[148],[60,40247,40248,40251],{"style":1940},[60,40249],{"className":40250,"style":325},[156],[60,40252,40254],{"className":40253},[161,162,163,164],[60,40255,23005],{"className":40256},[127,178,164],[60,40258,213],{"className":40259},[212],[60,40261,40263],{"className":40262},[144],[60,40264,40266],{"className":40265,"style":341},[148],[60,40267],{},[60,40269,40271,40337],{"className":40270},[63],[60,40272,40274],{"className":40273},[67],[69,40275,40276],{"xmlns":71},[73,40277,40278,40334],{},[76,40279,40280,40292,40294,40300,40316,40318,40320,40322,40328,40330,40332],{},[550,40281,40282,40284],{},[84,40283,359],{},[76,40285,40286,40288,40290],{},[397,40287,400],{"stretchy":399},[84,40289,16342],{},[397,40291,405],{"stretchy":399},[397,40293,990],{},[96,40295,40296,40298],{},[84,40297,16644],{},[102,40299,820],{},[550,40301,40302,40304],{},[84,40303,359],{},[76,40305,40306,40308,40310,40312,40314],{},[397,40307,400],{"stretchy":399},[84,40309,16342],{},[397,40311,817],{},[102,40313,820],{},[397,40315,405],{"stretchy":399},[397,40317,990],{},[397,40319,16359],{},[397,40321,990],{},[96,40323,40324,40326],{},[84,40325,16644],{},[84,40327,16342],{},[84,40329,359],{},[397,40331,448],{},[102,40333,104],{},[106,40335,40336],{"encoding":108},"x^{(n)} + a_1 x^{(n-1)} + \\cdots + a_n x = 0",[60,40338,40340,40395,40495,40513,40571],{"className":40339,"ariaHidden":114},[113],[60,40341,40343,40347,40386,40389,40392],{"className":40342},[118],[60,40344],{"className":40345,"style":40346},[122],"height:0.9713em;vertical-align:-0.0833em;",[60,40348,40350,40353],{"className":40349},[127],[60,40351,359],{"className":40352},[127,178],[60,40354,40356],{"className":40355},[183],[60,40357,40359],{"className":40358},[139],[60,40360,40362],{"className":40361},[144],[60,40363,40366],{"className":40364,"style":40365},[148],"height:0.888em;",[60,40367,40368,40371],{"style":608},[60,40369],{"className":40370,"style":325},[156],[60,40372,40374],{"className":40373},[161,162,163,164],[60,40375,40377,40380,40383],{"className":40376},[127,164],[60,40378,400],{"className":40379},[131,164],[60,40381,16342],{"className":40382},[127,178,164],[60,40384,405],{"className":40385},[267,164],[60,40387],{"className":40388,"style":924},[469],[60,40390,990],{"className":40391},[928],[60,40393],{"className":40394,"style":924},[469],[60,40396,40398,40402,40442,40486,40489,40492],{"className":40397},[118],[60,40399],{"className":40400,"style":40401},[122],"height:1.038em;vertical-align:-0.15em;",[60,40403,40405,40408],{"className":40404},[127],[60,40406,16644],{"className":40407},[127,178],[60,40409,40411],{"className":40410},[183],[60,40412,40414,40434],{"className":40413},[139,140],[60,40415,40417,40431],{"className":40416},[144],[60,40418,40420],{"className":40419,"style":318},[148],[60,40421,40422,40425],{"style":1940},[60,40423],{"className":40424,"style":325},[156],[60,40426,40428],{"className":40427},[161,162,163,164],[60,40429,820],{"className":40430},[127,164],[60,40432,213],{"className":40433},[212],[60,40435,40437],{"className":40436},[144],[60,40438,40440],{"className":40439,"style":341},[148],[60,40441],{},[60,40443,40445,40448],{"className":40444},[127],[60,40446,359],{"className":40447},[127,178],[60,40449,40451],{"className":40450},[183],[60,40452,40454],{"className":40453},[139],[60,40455,40457],{"className":40456},[144],[60,40458,40460],{"className":40459,"style":40365},[148],[60,40461,40462,40465],{"style":608},[60,40463],{"className":40464,"style":325},[156],[60,40466,40468],{"className":40467},[161,162,163,164],[60,40469,40471,40474,40477,40480,40483],{"className":40470},[127,164],[60,40472,400],{"className":40473},[131,164],[60,40475,16342],{"className":40476},[127,178,164],[60,40478,817],{"className":40479},[928,164],[60,40481,820],{"className":40482},[127,164],[60,40484,405],{"className":40485},[267,164],[60,40487],{"className":40488,"style":924},[469],[60,40490,990],{"className":40491},[928],[60,40493],{"className":40494,"style":924},[469],[60,40496,40498,40501,40504,40507,40510],{"className":40497},[118],[60,40499],{"className":40500,"style":17099},[122],[60,40502,16359],{"className":40503},[2326],[60,40505],{"className":40506,"style":924},[469],[60,40508,990],{"className":40509},[928],[60,40511],{"className":40512,"style":924},[469],[60,40514,40516,40519,40559,40562,40565,40568],{"className":40515},[118],[60,40517],{"className":40518,"style":2734},[122],[60,40520,40522,40525],{"className":40521},[127],[60,40523,16644],{"className":40524},[127,178],[60,40526,40528],{"className":40527},[183],[60,40529,40531,40551],{"className":40530},[139,140],[60,40532,40534,40548],{"className":40533},[144],[60,40535,40537],{"className":40536,"style":17136},[148],[60,40538,40539,40542],{"style":1940},[60,40540],{"className":40541,"style":325},[156],[60,40543,40545],{"className":40544},[161,162,163,164],[60,40546,16342],{"className":40547},[127,178,164],[60,40549,213],{"className":40550},[212],[60,40552,40554],{"className":40553},[144],[60,40555,40557],{"className":40556,"style":341},[148],[60,40558],{},[60,40560,359],{"className":40561},[127,178],[60,40563],{"className":40564,"style":470},[469],[60,40566,448],{"className":40567},[474],[60,40569],{"className":40570,"style":470},[469],[60,40572,40574,40577],{"className":40573},[118],[60,40575],{"className":40576,"style":484},[122],[60,40578,104],{"className":40579},[127]," 的解，所以：\n",[60,40582,40584,40656],{"className":40583},[63],[60,40585,40587],{"className":40586},[67],[69,40588,40589],{"xmlns":71},[73,40590,40591,40653],{},[76,40592,40593,40607,40609,40611,40617,40635,40637,40639,40641,40647],{},[2127,40594,40595,40597,40599],{},[84,40596,359],{},[84,40598,23005],{},[76,40600,40601,40603,40605],{},[397,40602,400],{"stretchy":399},[84,40604,16342],{},[397,40606,405],{"stretchy":399},[397,40608,448],{},[397,40610,817],{},[96,40612,40613,40615],{},[84,40614,16644],{},[102,40616,820],{},[2127,40618,40619,40621,40623],{},[84,40620,359],{},[84,40622,23005],{},[76,40624,40625,40627,40629,40631,40633],{},[397,40626,400],{"stretchy":399},[84,40628,16342],{},[397,40630,817],{},[102,40632,820],{},[397,40634,405],{"stretchy":399},[397,40636,817],{},[397,40638,16359],{},[397,40640,817],{},[96,40642,40643,40645],{},[84,40644,16644],{},[84,40646,16342],{},[96,40648,40649,40651],{},[84,40650,359],{},[84,40652,23005],{},[106,40654,40655],{"encoding":108},"x_i^{(n)} = -a_1 x_i^{(n-1)} - \\cdots - a_n x_i",[60,40657,40659,40734,40858,40876],{"className":40658,"ariaHidden":114},[113],[60,40660,40662,40665,40725,40728,40731],{"className":40661},[118],[60,40663],{"className":40664,"style":38986},[122],[60,40666,40668,40671],{"className":40667},[127],[60,40669,359],{"className":40670},[127,178],[60,40672,40674],{"className":40673},[183],[60,40675,40677,40717],{"className":40676},[139,140],[60,40678,40680,40714],{"className":40679},[144],[60,40681,40683,40694],{"className":40682,"style":39005},[148],[60,40684,40685,40688],{"style":39008},[60,40686],{"className":40687,"style":325},[156],[60,40689,40691],{"className":40690},[161,162,163,164],[60,40692,23005],{"className":40693},[127,178,164],[60,40695,40696,40699],{"style":39020},[60,40697],{"className":40698,"style":325},[156],[60,40700,40702],{"className":40701},[161,162,163,164],[60,40703,40705,40708,40711],{"className":40704},[127,164],[60,40706,400],{"className":40707},[131,164],[60,40709,16342],{"className":40710},[127,178,164],[60,40712,405],{"className":40713},[267,164],[60,40715,213],{"className":40716},[212],[60,40718,40720],{"className":40719},[144],[60,40721,40723],{"className":40722,"style":39054},[148],[60,40724],{},[60,40726],{"className":40727,"style":470},[469],[60,40729,448],{"className":40730},[474],[60,40732],{"className":40733,"style":470},[469],[60,40735,40737,40740,40743,40783,40849,40852,40855],{"className":40736},[118],[60,40738],{"className":40739,"style":38986},[122],[60,40741,817],{"className":40742},[127],[60,40744,40746,40749],{"className":40745},[127],[60,40747,16644],{"className":40748},[127,178],[60,40750,40752],{"className":40751},[183],[60,40753,40755,40775],{"className":40754},[139,140],[60,40756,40758,40772],{"className":40757},[144],[60,40759,40761],{"className":40760,"style":318},[148],[60,40762,40763,40766],{"style":1940},[60,40764],{"className":40765,"style":325},[156],[60,40767,40769],{"className":40768},[161,162,163,164],[60,40770,820],{"className":40771},[127,164],[60,40773,213],{"className":40774},[212],[60,40776,40778],{"className":40777},[144],[60,40779,40781],{"className":40780,"style":341},[148],[60,40782],{},[60,40784,40786,40789],{"className":40785},[127],[60,40787,359],{"className":40788},[127,178],[60,40790,40792],{"className":40791},[183],[60,40793,40795,40841],{"className":40794},[139,140],[60,40796,40798,40838],{"className":40797},[144],[60,40799,40801,40812],{"className":40800,"style":39005},[148],[60,40802,40803,40806],{"style":39008},[60,40804],{"className":40805,"style":325},[156],[60,40807,40809],{"className":40808},[161,162,163,164],[60,40810,23005],{"className":40811},[127,178,164],[60,40813,40814,40817],{"style":39020},[60,40815],{"className":40816,"style":325},[156],[60,40818,40820],{"className":40819},[161,162,163,164],[60,40821,40823,40826,40829,40832,40835],{"className":40822},[127,164],[60,40824,400],{"className":40825},[131,164],[60,40827,16342],{"className":40828},[127,178,164],[60,40830,817],{"className":40831},[928,164],[60,40833,820],{"className":40834},[127,164],[60,40836,405],{"className":40837},[267,164],[60,40839,213],{"className":40840},[212],[60,40842,40844],{"className":40843},[144],[60,40845,40847],{"className":40846,"style":39054},[148],[60,40848],{},[60,40850],{"className":40851,"style":924},[469],[60,40853,817],{"className":40854},[928],[60,40856],{"className":40857,"style":924},[469],[60,40859,40861,40864,40867,40870,40873],{"className":40860},[118],[60,40862],{"className":40863,"style":17099},[122],[60,40865,16359],{"className":40866},[2326],[60,40868],{"className":40869,"style":924},[469],[60,40871,817],{"className":40872},[928],[60,40874],{"className":40875,"style":924},[469],[60,40877,40879,40882,40922],{"className":40878},[118],[60,40880],{"className":40881,"style":2734},[122],[60,40883,40885,40888],{"className":40884},[127],[60,40886,16644],{"className":40887},[127,178],[60,40889,40891],{"className":40890},[183],[60,40892,40894,40914],{"className":40893},[139,140],[60,40895,40897,40911],{"className":40896},[144],[60,40898,40900],{"className":40899,"style":17136},[148],[60,40901,40902,40905],{"style":1940},[60,40903],{"className":40904,"style":325},[156],[60,40906,40908],{"className":40907},[161,162,163,164],[60,40909,16342],{"className":40910},[127,178,164],[60,40912,213],{"className":40913},[212],[60,40915,40917],{"className":40916},[144],[60,40918,40920],{"className":40919,"style":341},[148],[60,40921],{},[60,40923,40925,40928],{"className":40924},[127],[60,40926,359],{"className":40927},[127,178],[60,40929,40931],{"className":40930},[183],[60,40932,40934,40954],{"className":40933},[139,140],[60,40935,40937,40951],{"className":40936},[144],[60,40938,40940],{"className":40939,"style":38830},[148],[60,40941,40942,40945],{"style":1940},[60,40943],{"className":40944,"style":325},[156],[60,40946,40948],{"className":40947},[161,162,163,164],[60,40949,23005],{"className":40950},[127,178,164],[60,40952,213],{"className":40953},[212],[60,40955,40957],{"className":40956},[144],[60,40958,40960],{"className":40959,"style":341},[148],[60,40961],{},[33,40963,40964,40965,41027,41028,41187,41188,41309],{},"把这个代入到 ",[60,40966,40968,40986],{"className":40967},[63],[60,40969,40971],{"className":40970},[67],[69,40972,40973],{"xmlns":71},[73,40974,40975,40983],{},[76,40976,40977],{},[550,40978,40979,40981],{},[84,40980,38746],{},[397,40982,557],{"mathvariant":86,"lspace":556,"rspace":556},[106,40984,40985],{"encoding":108},"W'",[60,40987,40989],{"className":40988,"ariaHidden":114},[113],[60,40990,40992,40995],{"className":40991},[118],[60,40993],{"className":40994,"style":605},[122],[60,40996,40998,41001],{"className":40997},[127],[60,40999,38746],{"className":41000,"style":3572},[127,178],[60,41002,41004],{"className":41003},[183],[60,41005,41007],{"className":41006},[139],[60,41008,41010],{"className":41009},[144],[60,41011,41013],{"className":41012,"style":605},[148],[60,41014,41015,41018],{"style":608},[60,41016],{"className":41017,"style":325},[156],[60,41019,41021],{"className":41020},[161,162,163,164],[60,41022,41024],{"className":41023},[127,164],[60,41025,557],{"className":41026},[127,164]," 的最后一行。利用行列式拆分性质，只有包含 ",[60,41029,41031,41069],{"className":41030},[63],[60,41032,41034],{"className":41033},[67],[69,41035,41036],{"xmlns":71},[73,41037,41038,41066],{},[76,41039,41040,41042,41048],{},[397,41041,817],{},[96,41043,41044,41046],{},[84,41045,16644],{},[102,41047,820],{},[2127,41049,41050,41052,41054],{},[84,41051,359],{},[84,41053,23005],{},[76,41055,41056,41058,41060,41062,41064],{},[397,41057,400],{"stretchy":399},[84,41059,16342],{},[397,41061,817],{},[102,41063,820],{},[397,41065,405],{"stretchy":399},[106,41067,41068],{"encoding":108},"-a_1 x_i^{(n-1)}",[60,41070,41072],{"className":41071,"ariaHidden":114},[113],[60,41073,41075,41078,41081,41121],{"className":41074},[118],[60,41076],{"className":41077,"style":38986},[122],[60,41079,817],{"className":41080},[127],[60,41082,41084,41087],{"className":41083},[127],[60,41085,16644],{"className":41086},[127,178],[60,41088,41090],{"className":41089},[183],[60,41091,41093,41113],{"className":41092},[139,140],[60,41094,41096,41110],{"className":41095},[144],[60,41097,41099],{"className":41098,"style":318},[148],[60,41100,41101,41104],{"style":1940},[60,41102],{"className":41103,"style":325},[156],[60,41105,41107],{"className":41106},[161,162,163,164],[60,41108,820],{"className":41109},[127,164],[60,41111,213],{"className":41112},[212],[60,41114,41116],{"className":41115},[144],[60,41117,41119],{"className":41118,"style":341},[148],[60,41120],{},[60,41122,41124,41127],{"className":41123},[127],[60,41125,359],{"className":41126},[127,178],[60,41128,41130],{"className":41129},[183],[60,41131,41133,41179],{"className":41132},[139,140],[60,41134,41136,41176],{"className":41135},[144],[60,41137,41139,41150],{"className":41138,"style":39005},[148],[60,41140,41141,41144],{"style":39008},[60,41142],{"className":41143,"style":325},[156],[60,41145,41147],{"className":41146},[161,162,163,164],[60,41148,23005],{"className":41149},[127,178,164],[60,41151,41152,41155],{"style":39020},[60,41153],{"className":41154,"style":325},[156],[60,41156,41158],{"className":41157},[161,162,163,164],[60,41159,41161,41164,41167,41170,41173],{"className":41160},[127,164],[60,41162,400],{"className":41163},[131,164],[60,41165,16342],{"className":41166},[127,178,164],[60,41168,817],{"className":41169},[928,164],[60,41171,820],{"className":41172},[127,164],[60,41174,405],{"className":41175},[267,164],[60,41177,213],{"className":41178},[212],[60,41180,41182],{"className":41181},[144],[60,41183,41185],{"className":41184,"style":39054},[148],[60,41186],{}," 的那一项是非零的（因为其他的项如 ",[60,41189,41191,41217],{"className":41190},[63],[60,41192,41194],{"className":41193},[67],[69,41195,41196],{"xmlns":71},[73,41197,41198,41214],{},[76,41199,41200,41202,41208],{},[397,41201,817],{},[96,41203,41204,41206],{},[84,41205,16644],{},[84,41207,16342],{},[96,41209,41210,41212],{},[84,41211,359],{},[84,41213,23005],{},[106,41215,41216],{"encoding":108},"-a_n x_i",[60,41218,41220],{"className":41219,"ariaHidden":114},[113],[60,41221,41223,41226,41229,41269],{"className":41222},[118],[60,41224],{"className":41225,"style":16079},[122],[60,41227,817],{"className":41228},[127],[60,41230,41232,41235],{"className":41231},[127],[60,41233,16644],{"className":41234},[127,178],[60,41236,41238],{"className":41237},[183],[60,41239,41241,41261],{"className":41240},[139,140],[60,41242,41244,41258],{"className":41243},[144],[60,41245,41247],{"className":41246,"style":17136},[148],[60,41248,41249,41252],{"style":1940},[60,41250],{"className":41251,"style":325},[156],[60,41253,41255],{"className":41254},[161,162,163,164],[60,41256,16342],{"className":41257},[127,178,164],[60,41259,213],{"className":41260},[212],[60,41262,41264],{"className":41263},[144],[60,41265,41267],{"className":41266,"style":341},[148],[60,41268],{},[60,41270,41272,41275],{"className":41271},[127],[60,41273,359],{"className":41274},[127,178],[60,41276,41278],{"className":41277},[183],[60,41279,41281,41301],{"className":41280},[139,140],[60,41282,41284,41298],{"className":41283},[144],[60,41285,41287],{"className":41286,"style":38830},[148],[60,41288,41289,41292],{"style":1940},[60,41290],{"className":41291,"style":325},[156],[60,41293,41295],{"className":41294},[161,162,163,164],[60,41296,23005],{"className":41297},[127,178,164],[60,41299,213],{"className":41300},[212],[60,41302,41304],{"className":41303},[144],[60,41305,41307],{"className":41306,"style":341},[148],[60,41308],{}," 会让最后一行和第一行成比例，行列式为0）。",[33,41311,41312,41313,41388,41389,488],{},"提取公因子 ",[60,41314,41316,41336],{"className":41315},[63],[60,41317,41319],{"className":41318},[67],[69,41320,41321],{"xmlns":71},[73,41322,41323,41333],{},[76,41324,41325,41327],{},[397,41326,817],{},[96,41328,41329,41331],{},[84,41330,16644],{},[102,41332,820],{},[106,41334,41335],{"encoding":108},"-a_1",[60,41337,41339],{"className":41338,"ariaHidden":114},[113],[60,41340,41342,41345,41348],{"className":41341},[118],[60,41343],{"className":41344,"style":16079},[122],[60,41346,817],{"className":41347},[127],[60,41349,41351,41354],{"className":41350},[127],[60,41352,16644],{"className":41353},[127,178],[60,41355,41357],{"className":41356},[183],[60,41358,41360,41380],{"className":41359},[139,140],[60,41361,41363,41377],{"className":41362},[144],[60,41364,41366],{"className":41365,"style":318},[148],[60,41367,41368,41371],{"style":1940},[60,41369],{"className":41370,"style":325},[156],[60,41372,41374],{"className":41373},[161,162,163,164],[60,41375,820],{"className":41376},[127,164],[60,41378,213],{"className":41379},[212],[60,41381,41383],{"className":41382},[144],[60,41384,41386],{"className":41385,"style":341},[148],[60,41387],{},"，剩下的正是原行列式 ",[60,41390,41392,41411],{"className":41391},[63],[60,41393,41395],{"className":41394},[67],[69,41396,41397],{"xmlns":71},[73,41398,41399,41409],{},[76,41400,41401,41403,41405,41407],{},[84,41402,38746],{},[397,41404,400],{"stretchy":399},[84,41406,2152],{},[397,41408,405],{"stretchy":399},[106,41410,38755],{"encoding":108},[60,41412,41414],{"className":41413,"ariaHidden":114},[113],[60,41415,41417,41420,41423,41426,41429],{"className":41416},[118],[60,41418],{"className":41419,"style":418},[122],[60,41421,38746],{"className":41422,"style":3572},[127,178],[60,41424,400],{"className":41425},[131],[60,41427,2152],{"className":41428},[127,178],[60,41430,405],{"className":41431},[267],[33,41433,41434,15718,41437,41587],{},[26,41435,41436],{},"结论",[60,41438,41440,41476],{"className":41439},[63],[60,41441,41443],{"className":41442},[67],[69,41444,41445],{"xmlns":71},[73,41446,41447,41473],{},[76,41448,41449,41455,41457,41459,41465,41467,41469,41471],{},[550,41450,41451,41453],{},[84,41452,38746],{},[397,41454,557],{"mathvariant":86,"lspace":556,"rspace":556},[397,41456,448],{},[397,41458,817],{},[96,41460,41461,41463],{},[84,41462,16644],{},[102,41464,820],{},[397,41466,400],{"stretchy":399},[84,41468,2152],{},[397,41470,405],{"stretchy":399},[84,41472,38746],{},[106,41474,41475],{"encoding":108},"W' = -a_1(t) W",[60,41477,41479,41526],{"className":41478,"ariaHidden":114},[113],[60,41480,41482,41485,41517,41520,41523],{"className":41481},[118],[60,41483],{"className":41484,"style":605},[122],[60,41486,41488,41491],{"className":41487},[127],[60,41489,38746],{"className":41490,"style":3572},[127,178],[60,41492,41494],{"className":41493},[183],[60,41495,41497],{"className":41496},[139],[60,41498,41500],{"className":41499},[144],[60,41501,41503],{"className":41502,"style":605},[148],[60,41504,41505,41508],{"style":608},[60,41506],{"className":41507,"style":325},[156],[60,41509,41511],{"className":41510},[161,162,163,164],[60,41512,41514],{"className":41513},[127,164],[60,41515,557],{"className":41516},[127,164],[60,41518],{"className":41519,"style":470},[469],[60,41521,448],{"className":41522},[474],[60,41524],{"className":41525,"style":470},[469],[60,41527,41529,41532,41535,41575,41578,41581,41584],{"className":41528},[118],[60,41530],{"className":41531,"style":418},[122],[60,41533,817],{"className":41534},[127],[60,41536,41538,41541],{"className":41537},[127],[60,41539,16644],{"className":41540},[127,178],[60,41542,41544],{"className":41543},[183],[60,41545,41547,41567],{"className":41546},[139,140],[60,41548,41550,41564],{"className":41549},[144],[60,41551,41553],{"className":41552,"style":318},[148],[60,41554,41555,41558],{"style":1940},[60,41556],{"className":41557,"style":325},[156],[60,41559,41561],{"className":41560},[161,162,163,164],[60,41562,820],{"className":41563},[127,164],[60,41565,213],{"className":41566},[212],[60,41568,41570],{"className":41569},[144],[60,41571,41573],{"className":41572,"style":341},[148],[60,41574],{},[60,41576,400],{"className":41577},[131],[60,41579,2152],{"className":41580},[127,178],[60,41582,405],{"className":41583},[267],[60,41585,38746],{"className":41586,"style":3572},[127,178],"。这是一个简单的一阶方程，解它就得到公式。",[15,41589],{},[18,41591,41593],{"id":41592},"_7-证明-n-阶非齐次方程最多有-n1-个线性无关解","7. 证明 n 阶非齐次方程最多有 n+1 个线性无关解",[23,41595,41596,41599,41600,41651],{},[26,41597,41598],{},"直觉理解：","\n想象三维空间（",[60,41601,41603,41621],{"className":41602},[63],[60,41604,41606],{"className":41605},[67],[69,41607,41608],{"xmlns":71},[73,41609,41610,41618],{},[76,41611,41612,41614,41616],{},[84,41613,16342],{},[397,41615,448],{},[102,41617,1474],{},[106,41619,41620],{"encoding":108},"n=3",[60,41622,41624,41642],{"className":41623,"ariaHidden":114},[113],[60,41625,41627,41630,41633,41636,41639],{"className":41626},[118],[60,41628],{"className":41629,"style":371},[122],[60,41631,16342],{"className":41632},[127,178],[60,41634],{"className":41635,"style":470},[469],[60,41637,448],{"className":41638},[474],[60,41640],{"className":41641,"style":470},[469],[60,41643,41645,41648],{"className":41644},[118],[60,41646],{"className":41647,"style":484},[122],[60,41649,1474],{"className":41650},[127],"）里的一个平面。",[51,41653,41654,41657,41660],{},[33,41655,41656],{},"齐次方程的解通过原点，构成一个平面（3维线性空间）。",[33,41658,41659],{},"非齐次方程的解，就是这个平面平移了一下（不过原点）。",[33,41661,41662],{},"在这个平移后的平面上找点，你最多能找几个点，使得它们不“共面\u002F共线”？",[23,41664,41665],{},[26,41666,41667],{},"证明逻辑：",[30,41669,41670,42459],{},[33,41671,41672,41675,41676,41704,41705,41845,41846,41907,41908,42406,42407,42458],{},[26,41673,41674],{},"存在性","：取齐次方程的 ",[60,41677,41679,41692],{"className":41678},[63],[60,41680,41682],{"className":41681},[67],[69,41683,41684],{"xmlns":71},[73,41685,41686,41690],{},[76,41687,41688],{},[84,41689,16342],{},[106,41691,16342],{"encoding":108},[60,41693,41695],{"className":41694,"ariaHidden":114},[113],[60,41696,41698,41701],{"className":41697},[118],[60,41699],{"className":41700,"style":371},[122],[60,41702,16342],{"className":41703},[127,178]," 个线性无关解 ",[60,41706,41708,41738],{"className":41707},[63],[60,41709,41711],{"className":41710},[67],[69,41712,41713],{"xmlns":71},[73,41714,41715,41735],{},[76,41716,41717,41723,41725,41727,41729],{},[96,41718,41719,41721],{},[84,41720,359],{},[102,41722,820],{},[397,41724,569],{"separator":114},[397,41726,15469],{},[397,41728,569],{"separator":114},[96,41730,41731,41733],{},[84,41732,359],{},[84,41734,16342],{},[106,41736,41737],{"encoding":108},"x_1, \\dots, x_n",[60,41739,41741],{"className":41740,"ariaHidden":114},[113],[60,41742,41744,41747,41787,41790,41793,41796,41799,41802,41805],{"className":41743},[118],[60,41745],{"className":41746,"style":299},[122],[60,41748,41750,41753],{"className":41749},[127],[60,41751,359],{"className":41752},[127,178],[60,41754,41756],{"className":41755},[183],[60,41757,41759,41779],{"className":41758},[139,140],[60,41760,41762,41776],{"className":41761},[144],[60,41763,41765],{"className":41764,"style":318},[148],[60,41766,41767,41770],{"style":1940},[60,41768],{"className":41769,"style":325},[156],[60,41771,41773],{"className":41772},[161,162,163,164],[60,41774,820],{"className":41775},[127,164],[60,41777,213],{"className":41778},[212],[60,41780,41782],{"className":41781},[144],[60,41783,41785],{"className":41784,"style":341},[148],[60,41786],{},[60,41788,569],{"className":41789},[649],[60,41791],{"className":41792,"style":653},[469],[60,41794,15469],{"className":41795},[2326],[60,41797],{"className":41798,"style":653},[469],[60,41800,569],{"className":41801},[649],[60,41803],{"className":41804,"style":653},[469],[60,41806,41808,41811],{"className":41807},[127],[60,41809,359],{"className":41810},[127,178],[60,41812,41814],{"className":41813},[183],[60,41815,41817,41837],{"className":41816},[139,140],[60,41818,41820,41834],{"className":41819},[144],[60,41821,41823],{"className":41822,"style":17136},[148],[60,41824,41825,41828],{"style":1940},[60,41826],{"className":41827,"style":325},[156],[60,41829,41831],{"className":41830},[161,162,163,164],[60,41832,16342],{"className":41833},[127,178,164],[60,41835,213],{"className":41836},[212],[60,41838,41840],{"className":41839},[144],[60,41841,41843],{"className":41842,"style":341},[148],[60,41844],{}," 和非齐次方程的一个特解 ",[60,41847,41849,41867],{"className":41848},[63],[60,41850,41852],{"className":41851},[67],[69,41853,41854],{"xmlns":71},[73,41855,41856,41864],{},[76,41857,41858],{},[25516,41859,41860,41862],{"accent":114},[84,41861,359],{},[397,41863,25522],{},[106,41865,41866],{"encoding":108},"\\bar{x}",[60,41868,41870],{"className":41869,"ariaHidden":114},[113],[60,41871,41873,41876],{"className":41872},[118],[60,41874],{"className":41875,"style":25607},[122],[60,41877,41879],{"className":41878},[127,25611],[60,41880,41882],{"className":41881},[139],[60,41883,41885],{"className":41884},[144],[60,41886,41888,41896],{"className":41887,"style":25607},[148],[60,41889,41890,41893],{"style":19374},[60,41891],{"className":41892,"style":157},[156],[60,41894,359],{"className":41895},[127,178],[60,41897,41898,41901],{"style":19374},[60,41899],{"className":41900,"style":157},[156],[60,41902,41904],{"className":41903,"style":25638},[25637],[60,41905,25522],{"className":41906},[127],"。\n构造 ",[60,41909,41911,41995],{"className":41910},[63],[60,41912,41914],{"className":41913},[67],[69,41915,41916],{"xmlns":71},[73,41917,41918,41992],{},[76,41919,41920,41926,41928,41934,41936,41938,41944,41946,41952,41954,41960,41962,41964,41966,41968,41970,41976,41978,41984,41986],{},[96,41921,41922,41924],{},[84,41923,100],{},[102,41925,104],{},[397,41927,448],{},[25516,41929,41930,41932],{"accent":114},[84,41931,359],{},[397,41933,25522],{},[397,41935,569],{"separator":114},[13095,41937,13471],{},[96,41939,41940,41942],{},[84,41941,100],{},[102,41943,820],{},[397,41945,448],{},[25516,41947,41948,41950],{"accent":114},[84,41949,359],{},[397,41951,25522],{},[397,41953,990],{},[96,41955,41956,41958],{},[84,41957,359],{},[102,41959,820],{},[397,41961,569],{"separator":114},[13095,41963,13471],{},[397,41965,15469],{},[397,41967,569],{"separator":114},[13095,41969,13471],{},[96,41971,41972,41974],{},[84,41973,100],{},[84,41975,16342],{},[397,41977,448],{},[25516,41979,41980,41982],{"accent":114},[84,41981,359],{},[397,41983,25522],{},[397,41985,990],{},[96,41987,41988,41990],{},[84,41989,359],{},[84,41991,16342],{},[106,41993,41994],{"encoding":108},"y_0 = \\bar{x}, \\ y_1 = \\bar{x}+x_1, \\ \\dots, \\ y_n = \\bar{x}+x_n",[60,41996,41998,42053,42149,42195,42314,42360],{"className":41997,"ariaHidden":114},[113],[60,41999,42001,42004,42044,42047,42050],{"className":42000},[118],[60,42002],{"className":42003,"style":299},[122],[60,42005,42007,42010],{"className":42006},[127],[60,42008,100],{"className":42009,"style":179},[127,178],[60,42011,42013],{"className":42012},[183],[60,42014,42016,42036],{"className":42015},[139,140],[60,42017,42019,42033],{"className":42018},[144],[60,42020,42022],{"className":42021,"style":318},[148],[60,42023,42024,42027],{"style":321},[60,42025],{"className":42026,"style":325},[156],[60,42028,42030],{"className":42029},[161,162,163,164],[60,42031,104],{"className":42032},[127,164],[60,42034,213],{"className":42035},[212],[60,42037,42039],{"className":42038},[144],[60,42040,42042],{"className":42041,"style":341},[148],[60,42043],{},[60,42045],{"className":42046,"style":470},[469],[60,42048,448],{"className":42049},[474],[60,42051],{"className":42052,"style":470},[469],[60,42054,42056,42060,42091,42094,42097,42100,42140,42143,42146],{"className":42055},[118],[60,42057],{"className":42058,"style":42059},[122],"height:0.7622em;vertical-align:-0.1944em;",[60,42061,42063],{"className":42062},[127,25611],[60,42064,42066],{"className":42065},[139],[60,42067,42069],{"className":42068},[144],[60,42070,42072,42080],{"className":42071,"style":25607},[148],[60,42073,42074,42077],{"style":19374},[60,42075],{"className":42076,"style":157},[156],[60,42078,359],{"className":42079},[127,178],[60,42081,42082,42085],{"style":19374},[60,42083],{"className":42084,"style":157},[156],[60,42086,42088],{"className":42087,"style":25638},[25637],[60,42089,25522],{"className":42090},[127],[60,42092,569],{"className":42093},[649],[60,42095,13471],{"className":42096},[469],[60,42098],{"className":42099,"style":653},[469],[60,42101,42103,42106],{"className":42102},[127],[60,42104,100],{"className":42105,"style":179},[127,178],[60,42107,42109],{"className":42108},[183],[60,42110,42112,42132],{"className":42111},[139,140],[60,42113,42115,42129],{"className":42114},[144],[60,42116,42118],{"className":42117,"style":318},[148],[60,42119,42120,42123],{"style":321},[60,42121],{"className":42122,"style":325},[156],[60,42124,42126],{"className":42125},[161,162,163,164],[60,42127,820],{"className":42128},[127,164],[60,42130,213],{"className":42131},[212],[60,42133,42135],{"className":42134},[144],[60,42136,42138],{"className":42137,"style":341},[148],[60,42139],{},[60,42141],{"className":42142,"style":470},[469],[60,42144,448],{"className":42145},[474],[60,42147],{"className":42148,"style":470},[469],[60,42150,42152,42155,42186,42189,42192],{"className":42151},[118],[60,42153],{"className":42154,"style":17099},[122],[60,42156,42158],{"className":42157},[127,25611],[60,42159,42161],{"className":42160},[139],[60,42162,42164],{"className":42163},[144],[60,42165,42167,42175],{"className":42166,"style":25607},[148],[60,42168,42169,42172],{"style":19374},[60,42170],{"className":42171,"style":157},[156],[60,42173,359],{"className":42174},[127,178],[60,42176,42177,42180],{"style":19374},[60,42178],{"className":42179,"style":157},[156],[60,42181,42183],{"className":42182,"style":25638},[25637],[60,42184,25522],{"className":42185},[127],[60,42187],{"className":42188,"style":924},[469],[60,42190,990],{"className":42191},[928],[60,42193],{"className":42194,"style":924},[469],[60,42196,42198,42201,42241,42244,42247,42250,42253,42256,42259,42262,42265,42305,42308,42311],{"className":42197},[118],[60,42199],{"className":42200,"style":299},[122],[60,42202,42204,42207],{"className":42203},[127],[60,42205,359],{"className":42206},[127,178],[60,42208,42210],{"className":42209},[183],[60,42211,42213,42233],{"className":42212},[139,140],[60,42214,42216,42230],{"className":42215},[144],[60,42217,42219],{"className":42218,"style":318},[148],[60,42220,42221,42224],{"style":1940},[60,42222],{"className":42223,"style":325},[156],[60,42225,42227],{"className":42226},[161,162,163,164],[60,42228,820],{"className":42229},[127,164],[60,42231,213],{"className":42232},[212],[60,42234,42236],{"className":42235},[144],[60,42237,42239],{"className":42238,"style":341},[148],[60,42240],{},[60,42242,569],{"className":42243},[649],[60,42245,13471],{"className":42246},[469],[60,42248],{"className":42249,"style":653},[469],[60,42251,15469],{"className":42252},[2326],[60,42254],{"className":42255,"style":653},[469],[60,42257,569],{"className":42258},[649],[60,42260,13471],{"className":42261},[469],[60,42263],{"className":42264,"style":653},[469],[60,42266,42268,42271],{"className":42267},[127],[60,42269,100],{"className":42270,"style":179},[127,178],[60,42272,42274],{"className":42273},[183],[60,42275,42277,42297],{"className":42276},[139,140],[60,42278,42280,42294],{"className":42279},[144],[60,42281,42283],{"className":42282,"style":17136},[148],[60,42284,42285,42288],{"style":321},[60,42286],{"className":42287,"style":325},[156],[60,42289,42291],{"className":42290},[161,162,163,164],[60,42292,16342],{"className":42293},[127,178,164],[60,42295,213],{"className":42296},[212],[60,42298,42300],{"className":42299},[144],[60,42301,42303],{"className":42302,"style":341},[148],[60,42304],{},[60,42306],{"className":42307,"style":470},[469],[60,42309,448],{"className":42310},[474],[60,42312],{"className":42313,"style":470},[469],[60,42315,42317,42320,42351,42354,42357],{"className":42316},[118],[60,42318],{"className":42319,"style":17099},[122],[60,42321,42323],{"className":42322},[127,25611],[60,42324,42326],{"className":42325},[139],[60,42327,42329],{"className":42328},[144],[60,42330,42332,42340],{"className":42331,"style":25607},[148],[60,42333,42334,42337],{"style":19374},[60,42335],{"className":42336,"style":157},[156],[60,42338,359],{"className":42339},[127,178],[60,42341,42342,42345],{"style":19374},[60,42343],{"className":42344,"style":157},[156],[60,42346,42348],{"className":42347,"style":25638},[25637],[60,42349,25522],{"className":42350},[127],[60,42352],{"className":42353,"style":924},[469],[60,42355,990],{"className":42356},[928],[60,42358],{"className":42359,"style":924},[469],[60,42361,42363,42366],{"className":42362},[118],[60,42364],{"className":42365,"style":2734},[122],[60,42367,42369,42372],{"className":42368},[127],[60,42370,359],{"className":42371},[127,178],[60,42373,42375],{"className":42374},[183],[60,42376,42378,42398],{"className":42377},[139,140],[60,42379,42381,42395],{"className":42380},[144],[60,42382,42384],{"className":42383,"style":17136},[148],[60,42385,42386,42389],{"style":1940},[60,42387],{"className":42388,"style":325},[156],[60,42390,42392],{"className":42391},[161,162,163,164],[60,42393,16342],{"className":42394},[127,178,164],[60,42396,213],{"className":42397},[212],[60,42399,42401],{"className":42400},[144],[60,42402,42404],{"className":42403,"style":341},[148],[60,42405],{},"。\n这 ",[60,42408,42410,42428],{"className":42409},[63],[60,42411,42413],{"className":42412},[67],[69,42414,42415],{"xmlns":71},[73,42416,42417,42425],{},[76,42418,42419,42421,42423],{},[84,42420,16342],{},[397,42422,990],{},[102,42424,820],{},[106,42426,42427],{"encoding":108},"n+1",[60,42429,42431,42449],{"className":42430,"ariaHidden":114},[113],[60,42432,42434,42437,42440,42443,42446],{"className":42433},[118],[60,42435],{"className":42436,"style":17099},[122],[60,42438,16342],{"className":42439},[127,178],[60,42441],{"className":42442,"style":924},[469],[60,42444,990],{"className":42445},[928],[60,42447],{"className":42448,"style":924},[469],[60,42450,42452,42455],{"className":42451},[118],[60,42453],{"className":42454,"style":484},[122],[60,42456,820],{"className":42457},[127]," 个解是线性无关的。（可以用定义证）。",[33,42460,42461,42464,42465,42516,42517,42728,42729,42929,42930,42929,43126,43156,43157,43227,43228,43231,43232,43260,43261,43311,43312,43362,43363,43391,43392,43462,43463,43517],{},[26,42462,42463],{},"最多 n+1 个","：假设有 ",[60,42466,42468,42486],{"className":42467},[63],[60,42469,42471],{"className":42470},[67],[69,42472,42473],{"xmlns":71},[73,42474,42475,42483],{},[76,42476,42477,42479,42481],{},[84,42478,16342],{},[397,42480,990],{},[102,42482,814],{},[106,42484,42485],{"encoding":108},"n+2",[60,42487,42489,42507],{"className":42488,"ariaHidden":114},[113],[60,42490,42492,42495,42498,42501,42504],{"className":42491},[118],[60,42493],{"className":42494,"style":17099},[122],[60,42496,16342],{"className":42497},[127,178],[60,42499],{"className":42500,"style":924},[469],[60,42502,990],{"className":42503},[928],[60,42505],{"className":42506,"style":924},[469],[60,42508,42510,42513],{"className":42509},[118],[60,42511],{"className":42512,"style":484},[122],[60,42514,814],{"className":42515},[127]," 个解 ",[60,42518,42520,42564],{"className":42519},[63],[60,42521,42523],{"className":42522},[67],[69,42524,42525],{"xmlns":71},[73,42526,42527,42561],{},[76,42528,42529,42535,42537,42543,42545,42547,42549],{},[96,42530,42531,42533],{},[84,42532,100],{},[102,42534,820],{},[397,42536,569],{"separator":114},[96,42538,42539,42541],{},[84,42540,100],{},[102,42542,814],{},[397,42544,569],{"separator":114},[397,42546,15469],{},[397,42548,569],{"separator":114},[96,42550,42551,42553],{},[84,42552,100],{},[76,42554,42555,42557,42559],{},[84,42556,16342],{},[397,42558,990],{},[102,42560,814],{},[106,42562,42563],{"encoding":108},"y_1, y_2, \\dots, y_{n+2}",[60,42565,42567],{"className":42566,"ariaHidden":114},[113],[60,42568,42570,42574,42614,42617,42620,42660,42663,42666,42669,42672,42675,42678],{"className":42569},[118],[60,42571],{"className":42572,"style":42573},[122],"height:0.6389em;vertical-align:-0.2083em;",[60,42575,42577,42580],{"className":42576},[127],[60,42578,100],{"className":42579,"style":179},[127,178],[60,42581,42583],{"className":42582},[183],[60,42584,42586,42606],{"className":42585},[139,140],[60,42587,42589,42603],{"className":42588},[144],[60,42590,42592],{"className":42591,"style":318},[148],[60,42593,42594,42597],{"style":321},[60,42595],{"className":42596,"style":325},[156],[60,42598,42600],{"className":42599},[161,162,163,164],[60,42601,820],{"className":42602},[127,164],[60,42604,213],{"className":42605},[212],[60,42607,42609],{"className":42608},[144],[60,42610,42612],{"className":42611,"style":341},[148],[60,42613],{},[60,42615,569],{"className":42616},[649],[60,42618],{"className":42619,"style":653},[469],[60,42621,42623,42626],{"className":42622},[127],[60,42624,100],{"className":42625,"style":179},[127,178],[60,42627,42629],{"className":42628},[183],[60,42630,42632,42652],{"className":42631},[139,140],[60,42633,42635,42649],{"className":42634},[144],[60,42636,42638],{"className":42637,"style":318},[148],[60,42639,42640,42643],{"style":321},[60,42641],{"className":42642,"style":325},[156],[60,42644,42646],{"className":42645},[161,162,163,164],[60,42647,814],{"className":42648},[127,164],[60,42650,213],{"className":42651},[212],[60,42653,42655],{"className":42654},[144],[60,42656,42658],{"className":42657,"style":341},[148],[60,42659],{},[60,42661,569],{"className":42662},[649],[60,42664],{"className":42665,"style":653},[469],[60,42667,15469],{"className":42668},[2326],[60,42670],{"className":42671,"style":653},[469],[60,42673,569],{"className":42674},[649],[60,42676],{"className":42677,"style":653},[469],[60,42679,42681,42684],{"className":42680},[127],[60,42682,100],{"className":42683,"style":179},[127,178],[60,42685,42687],{"className":42686},[183],[60,42688,42690,42719],{"className":42689},[139,140],[60,42691,42693,42716],{"className":42692},[144],[60,42694,42696],{"className":42695,"style":318},[148],[60,42697,42698,42701],{"style":321},[60,42699],{"className":42700,"style":325},[156],[60,42702,42704],{"className":42703},[161,162,163,164],[60,42705,42707,42710,42713],{"className":42706},[127,164],[60,42708,16342],{"className":42709},[127,178,164],[60,42711,990],{"className":42712},[928,164],[60,42714,814],{"className":42715},[127,164],[60,42717,213],{"className":42718},[212],[60,42720,42722],{"className":42721},[144],[60,42723,42726],{"className":42724,"style":42725},[148],"height:0.2083em;",[60,42727],{},"。\n考虑它们的差：",[60,42730,42732,42767],{"className":42731},[63],[60,42733,42735],{"className":42734},[67],[69,42736,42737],{"xmlns":71},[73,42738,42739,42764],{},[76,42740,42741,42748,42750,42756,42758],{},[96,42742,42743,42746],{},[84,42744,42745],{},"z",[102,42747,820],{},[397,42749,448],{},[96,42751,42752,42754],{},[84,42753,100],{},[102,42755,814],{},[397,42757,817],{},[96,42759,42760,42762],{},[84,42761,100],{},[102,42763,820],{},[106,42765,42766],{"encoding":108},"z_1 = y_2 - y_1",[60,42768,42770,42827,42883],{"className":42769,"ariaHidden":114},[113],[60,42771,42773,42776,42818,42821,42824],{"className":42772},[118],[60,42774],{"className":42775,"style":2734},[122],[60,42777,42779,42783],{"className":42778},[127],[60,42780,42745],{"className":42781,"style":42782},[127,178],"margin-right:0.044em;",[60,42784,42786],{"className":42785},[183],[60,42787,42789,42810],{"className":42788},[139,140],[60,42790,42792,42807],{"className":42791},[144],[60,42793,42795],{"className":42794,"style":318},[148],[60,42796,42798,42801],{"style":42797},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[60,42799],{"className":42800,"style":325},[156],[60,42802,42804],{"className":42803},[161,162,163,164],[60,42805,820],{"className":42806},[127,164],[60,42808,213],{"className":42809},[212],[60,42811,42813],{"className":42812},[144],[60,42814,42816],{"className":42815,"style":341},[148],[60,42817],{},[60,42819],{"className":42820,"style":470},[469],[60,42822,448],{"className":42823},[474],[60,42825],{"className":42826,"style":470},[469],[60,42828,42830,42834,42874,42877,42880],{"className":42829},[118],[60,42831],{"className":42832,"style":42833},[122],"height:0.7778em;vertical-align:-0.1944em;",[60,42835,42837,42840],{"className":42836},[127],[60,42838,100],{"className":42839,"style":179},[127,178],[60,42841,42843],{"className":42842},[183],[60,42844,42846,42866],{"className":42845},[139,140],[60,42847,42849,42863],{"className":42848},[144],[60,42850,42852],{"className":42851,"style":318},[148],[60,42853,42854,42857],{"style":321},[60,42855],{"className":42856,"style":325},[156],[60,42858,42860],{"className":42859},[161,162,163,164],[60,42861,814],{"className":42862},[127,164],[60,42864,213],{"className":42865},[212],[60,42867,42869],{"className":42868},[144],[60,42870,42872],{"className":42871,"style":341},[148],[60,42873],{},[60,42875],{"className":42876,"style":924},[469],[60,42878,817],{"className":42879},[928],[60,42881],{"className":42882,"style":924},[469],[60,42884,42886,42889],{"className":42885},[118],[60,42887],{"className":42888,"style":299},[122],[60,42890,42892,42895],{"className":42891},[127],[60,42893,100],{"className":42894,"style":179},[127,178],[60,42896,42898],{"className":42897},[183],[60,42899,42901,42921],{"className":42900},[139,140],[60,42902,42904,42918],{"className":42903},[144],[60,42905,42907],{"className":42906,"style":318},[148],[60,42908,42909,42912],{"style":321},[60,42910],{"className":42911,"style":325},[156],[60,42913,42915],{"className":42914},[161,162,163,164],[60,42916,820],{"className":42917},[127,164],[60,42919,213],{"className":42920},[212],[60,42922,42924],{"className":42923},[144],[60,42925,42927],{"className":42926,"style":341},[148],[60,42928],{},", ",[60,42931,42933,42967],{"className":42932},[63],[60,42934,42936],{"className":42935},[67],[69,42937,42938],{"xmlns":71},[73,42939,42940,42964],{},[76,42941,42942,42948,42950,42956,42958],{},[96,42943,42944,42946],{},[84,42945,42745],{},[102,42947,814],{},[397,42949,448],{},[96,42951,42952,42954],{},[84,42953,100],{},[102,42955,1474],{},[397,42957,817],{},[96,42959,42960,42962],{},[84,42961,100],{},[102,42963,820],{},[106,42965,42966],{"encoding":108},"z_2 = y_3 - y_1",[60,42968,42970,43025,43080],{"className":42969,"ariaHidden":114},[113],[60,42971,42973,42976,43016,43019,43022],{"className":42972},[118],[60,42974],{"className":42975,"style":2734},[122],[60,42977,42979,42982],{"className":42978},[127],[60,42980,42745],{"className":42981,"style":42782},[127,178],[60,42983,42985],{"className":42984},[183],[60,42986,42988,43008],{"className":42987},[139,140],[60,42989,42991,43005],{"className":42990},[144],[60,42992,42994],{"className":42993,"style":318},[148],[60,42995,42996,42999],{"style":42797},[60,42997],{"className":42998,"style":325},[156],[60,43000,43002],{"className":43001},[161,162,163,164],[60,43003,814],{"className":43004},[127,164],[60,43006,213],{"className":43007},[212],[60,43009,43011],{"className":43010},[144],[60,43012,43014],{"className":43013,"style":341},[148],[60,43015],{},[60,43017],{"className":43018,"style":470},[469],[60,43020,448],{"className":43021},[474],[60,43023],{"className":43024,"style":470},[469],[60,43026,43028,43031,43071,43074,43077],{"className":43027},[118],[60,43029],{"className":43030,"style":42833},[122],[60,43032,43034,43037],{"className":43033},[127],[60,43035,100],{"className":43036,"style":179},[127,178],[60,43038,43040],{"className":43039},[183],[60,43041,43043,43063],{"className":43042},[139,140],[60,43044,43046,43060],{"className":43045},[144],[60,43047,43049],{"className":43048,"style":318},[148],[60,43050,43051,43054],{"style":321},[60,43052],{"className":43053,"style":325},[156],[60,43055,43057],{"className":43056},[161,162,163,164],[60,43058,1474],{"className":43059},[127,164],[60,43061,213],{"className":43062},[212],[60,43064,43066],{"className":43065},[144],[60,43067,43069],{"className":43068,"style":341},[148],[60,43070],{},[60,43072],{"className":43073,"style":924},[469],[60,43075,817],{"className":43076},[928],[60,43078],{"className":43079,"style":924},[469],[60,43081,43083,43086],{"className":43082},[118],[60,43084],{"className":43085,"style":299},[122],[60,43087,43089,43092],{"className":43088},[127],[60,43090,100],{"className":43091,"style":179},[127,178],[60,43093,43095],{"className":43094},[183],[60,43096,43098,43118],{"className":43097},[139,140],[60,43099,43101,43115],{"className":43100},[144],[60,43102,43104],{"className":43103,"style":318},[148],[60,43105,43106,43109],{"style":321},[60,43107],{"className":43108,"style":325},[156],[60,43110,43112],{"className":43111},[161,162,163,164],[60,43113,820],{"className":43114},[127,164],[60,43116,213],{"className":43117},[212],[60,43119,43121],{"className":43120},[144],[60,43122,43124],{"className":43123,"style":341},[148],[60,43125],{},[60,43127,43129,43143],{"className":43128},[63],[60,43130,43132],{"className":43131},[67],[69,43133,43134],{"xmlns":71},[73,43135,43136,43140],{},[76,43137,43138],{},[397,43139,15469],{},[106,43141,43142],{"encoding":108},"\\dots",[60,43144,43146],{"className":43145,"ariaHidden":114},[113],[60,43147,43149,43153],{"className":43148},[118],[60,43150],{"className":43151,"style":43152},[122],"height:0.123em;",[60,43154,15469],{"className":43155},[2326],".\n根据非齐次解的性质2，这些差 ",[60,43158,43160,43178],{"className":43159},[63],[60,43161,43163],{"className":43162},[67],[69,43164,43165],{"xmlns":71},[73,43166,43167,43175],{},[76,43168,43169],{},[96,43170,43171,43173],{},[84,43172,42745],{},[84,43174,23005],{},[106,43176,43177],{"encoding":108},"z_i",[60,43179,43181],{"className":43180,"ariaHidden":114},[113],[60,43182,43184,43187],{"className":43183},[118],[60,43185],{"className":43186,"style":2734},[122],[60,43188,43190,43193],{"className":43189},[127],[60,43191,42745],{"className":43192,"style":42782},[127,178],[60,43194,43196],{"className":43195},[183],[60,43197,43199,43219],{"className":43198},[139,140],[60,43200,43202,43216],{"className":43201},[144],[60,43203,43205],{"className":43204,"style":38830},[148],[60,43206,43207,43210],{"style":42797},[60,43208],{"className":43209,"style":325},[156],[60,43211,43213],{"className":43212},[161,162,163,164],[60,43214,23005],{"className":43215},[127,178,164],[60,43217,213],{"className":43218},[212],[60,43220,43222],{"className":43221},[144],[60,43223,43225],{"className":43224,"style":341},[148],[60,43226],{}," 都是",[26,43229,43230],{},"齐次方程的解","。\n齐次方程的解空间维度是 ",[60,43233,43235,43248],{"className":43234},[63],[60,43236,43238],{"className":43237},[67],[69,43239,43240],{"xmlns":71},[73,43241,43242,43246],{},[76,43243,43244],{},[84,43245,16342],{},[106,43247,16342],{"encoding":108},[60,43249,43251],{"className":43250,"ariaHidden":114},[113],[60,43252,43254,43257],{"className":43253},[118],[60,43255],{"className":43256,"style":371},[122],[60,43258,16342],{"className":43259},[127,178],"。\n如果你有 ",[60,43262,43264,43281],{"className":43263},[63],[60,43265,43267],{"className":43266},[67],[69,43268,43269],{"xmlns":71},[73,43270,43271,43279],{},[76,43272,43273,43275,43277],{},[84,43274,16342],{},[397,43276,990],{},[102,43278,820],{},[106,43280,42427],{"encoding":108},[60,43282,43284,43302],{"className":43283,"ariaHidden":114},[113],[60,43285,43287,43290,43293,43296,43299],{"className":43286},[118],[60,43288],{"className":43289,"style":17099},[122],[60,43291,16342],{"className":43292},[127,178],[60,43294],{"className":43295,"style":924},[469],[60,43297,990],{"className":43298},[928],[60,43300],{"className":43301,"style":924},[469],[60,43303,43305,43308],{"className":43304},[118],[60,43306],{"className":43307,"style":484},[122],[60,43309,820],{"className":43310},[127]," 个差向量（由 ",[60,43313,43315,43332],{"className":43314},[63],[60,43316,43318],{"className":43317},[67],[69,43319,43320],{"xmlns":71},[73,43321,43322,43330],{},[76,43323,43324,43326,43328],{},[84,43325,16342],{},[397,43327,990],{},[102,43329,814],{},[106,43331,42485],{"encoding":108},[60,43333,43335,43353],{"className":43334,"ariaHidden":114},[113],[60,43336,43338,43341,43344,43347,43350],{"className":43337},[118],[60,43339],{"className":43340,"style":17099},[122],[60,43342,16342],{"className":43343},[127,178],[60,43345],{"className":43346,"style":924},[469],[60,43348,990],{"className":43349},[928],[60,43351],{"className":43352,"style":924},[469],[60,43354,43356,43359],{"className":43355},[118],[60,43357],{"className":43358,"style":484},[122],[60,43360,814],{"className":43361},[127]," 个解产生），它们在 ",[60,43364,43366,43379],{"className":43365},[63],[60,43367,43369],{"className":43368},[67],[69,43370,43371],{"xmlns":71},[73,43372,43373,43377],{},[76,43374,43375],{},[84,43376,16342],{},[106,43378,16342],{"encoding":108},[60,43380,43382],{"className":43381,"ariaHidden":114},[113],[60,43383,43385,43388],{"className":43384},[118],[60,43386],{"className":43387,"style":371},[122],[60,43389,16342],{"className":43390},[127,178]," 维空间里必然线性相关。\n既然差向量线性相关，那么原解 ",[60,43393,43395,43413],{"className":43394},[63],[60,43396,43398],{"className":43397},[67],[69,43399,43400],{"xmlns":71},[73,43401,43402,43410],{},[76,43403,43404],{},[96,43405,43406,43408],{},[84,43407,100],{},[84,43409,23005],{},[106,43411,43412],{"encoding":108},"y_i",[60,43414,43416],{"className":43415,"ariaHidden":114},[113],[60,43417,43419,43422],{"className":43418},[118],[60,43420],{"className":43421,"style":299},[122],[60,43423,43425,43428],{"className":43424},[127],[60,43426,100],{"className":43427,"style":179},[127,178],[60,43429,43431],{"className":43430},[183],[60,43432,43434,43454],{"className":43433},[139,140],[60,43435,43437,43451],{"className":43436},[144],[60,43438,43440],{"className":43439,"style":38830},[148],[60,43441,43442,43445],{"style":321},[60,43443],{"className":43444,"style":325},[156],[60,43446,43448],{"className":43447},[161,162,163,164],[60,43449,23005],{"className":43450},[127,178,164],[60,43452,213],{"className":43453},[212],[60,43455,43457],{"className":43456},[144],[60,43458,43460],{"className":43459,"style":341},[148],[60,43461],{}," 也就线性相关了。\n",[26,43464,43465,43466,43516],{},"所以，不可能有 ",[60,43467,43469,43486],{"className":43468},[63],[60,43470,43472],{"className":43471},[67],[69,43473,43474],{"xmlns":71},[73,43475,43476,43484],{},[76,43477,43478,43480,43482],{},[84,43479,16342],{},[397,43481,990],{},[102,43483,814],{},[106,43485,42485],{"encoding":108},[60,43487,43489,43507],{"className":43488,"ariaHidden":114},[113],[60,43490,43492,43495,43498,43501,43504],{"className":43491},[118],[60,43493],{"className":43494,"style":17099},[122],[60,43496,16342],{"className":43497},[127,178],[60,43499],{"className":43500,"style":924},[469],[60,43502,990],{"className":43503},[928],[60,43505],{"className":43506,"style":924},[469],[60,43508,43510,43513],{"className":43509},[118],[60,43511],{"className":43512,"style":484},[122],[60,43514,814],{"className":43515},[127]," 个线性无关解。","\n希望这套详细的讲解能帮你打通任督二脉！如果哪个积分算不出来，或者哪个步骤卡住了，继续问！",{"title":43519,"searchDepth":43520,"depth":43520,"links":43521},"",2,[43522,43524,43525,43526,43527,43528,43529,43530,43531],{"id":20,"depth":43523,"text":21},3,{"id":493,"depth":43523,"text":494},{"id":3510,"depth":43523,"text":3511},{"id":15285,"depth":43523,"text":15285},{"id":15749,"depth":43523,"text":15750},{"id":19866,"depth":43523,"text":19867},{"id":34403,"depth":43523,"text":34404},{"id":38683,"depth":43523,"text":38684},{"id":41592,"depth":43523,"text":41593},"md",{"order":43520},true,"\u002Fsource\u002Fmath\u002Fode\u002F3-2and4-1-hw",{"title":5,"description":43519},"source\u002Fmath\u002Fode\u002F3-2&4-1 HW","ibz79D-JVs9rVN-hdVMHd3UjGeSBRSaop7erN_byzfA",1793692180213]