[{"data":1,"prerenderedAt":7030},["ShallowReactive",2],{"note:math\u002Fode\u002Freview":3,"site-search-catalogue":7029},{"id":4,"title":5,"body":6,"description":7009,"extension":7021,"meta":7022,"navigation":7024,"path":7025,"seo":7026,"stem":7027,"__hash__":7028},"notes\u002Fsource\u002Fmath\u002Fode\u002Freview.md","复习总结",{"type":7,"value":8,"toc":7008},"minimark",[9,14,21,273,276,596,600,605,609,1375,1380,3817,3821,3825,4580,4584,5716,5720,5724,6029,6034,6185,6190,6575,6610,7002,7005],[10,11,13],"h2",{"id":12},"一阶线性ode求解公式","一阶线性ODE求解公式",[15,16,17],"p",{},[18,19,20],"strong",{},"形式：",[15,22,23],{},[24,25,28,96],"span",{"className":26},[27],"katex",[24,29,32],{"className":30},[31],"katex-mathml",[33,34,36],"math",{"xmlns":35},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[37,38,39,91],"semantics",{},[40,41,42,61,65,68,72,74,77,79,82,85,87,89],"mrow",{},[43,44,45,54],"mfrac",{},[40,46,47,51],{},[48,49,50],"mi",{},"d",[48,52,53],{},"y",[40,55,56,58],{},[48,57,50],{},[48,59,60],{},"x",[62,63,64],"mo",{},"+",[48,66,67],{},"P",[62,69,71],{"stretchy":70},"false","(",[48,73,60],{},[62,75,76],{"stretchy":70},")",[48,78,53],{},[62,80,81],{},"=",[48,83,84],{},"Q",[62,86,71],{"stretchy":70},[48,88,60],{},[62,90,76],{"stretchy":70},[92,93,95],"annotation",{"encoding":94},"application\u002Fx-tex","\\frac{dy}{dx} + P(x)y = 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= e^{-\\int P(x) \\, dx} \\left( \\int Q(x) e^{\\int P(x) \\, dx} \\, dx + C \\right)",[24,377,379,398],{"className":378,"ariaHidden":100},[99],[24,380,382,386,389,392,395],{"className":381},[104],[24,383],{"className":384,"style":385},[108],"height:0.625em;vertical-align:-0.1944em;",[24,387,53],{"className":388,"style":190},[113,157],[24,390],{"className":391,"style":247},[212],[24,393,81],{"className":394},[251],[24,396],{"className":397,"style":247},[212],[24,399,401,405,476,480],{"className":400},[104],[24,402],{"className":403,"style":404},[108],"height:1.8em;vertical-align:-0.65em;",[24,406,408,411],{"className":407},[113],[24,409,299],{"className":410},[113,157],[24,412,415],{"className":413},[414],"msupsub",[24,416,418],{"className":417},[125],[24,419,421],{"className":420},[130],[24,422,425],{"className":423,"style":424},[134],"height:0.9265em;",[24,426,428,432],{"style":427},"top:-3.063em;margin-right:0.05em;",[24,429],{"className":430,"style":431},[142],"height:2.7em;",[24,433,435],{"className":434},[147,148,149,150],[24,436,438,441,445,452,455,458,461,464,467,470,473],{"className":437},[113,150],[24,439,304],{"className":440},[113,150],[24,442],{"className":443,"style":444},[212,150],"margin-right:0.1952em;",[24,446,307],{"className":447,"style":451},[448,449,450,150],"mop","op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[24,453],{"className":454,"style":444},[212,150],[24,456,67],{"className":457,"style":231},[113,157,150],[24,459,71],{"className":460},[117,150],[24,462,60],{"className":463},[113,157,150],[24,465,76],{"className":466},[208,150],[24,468],{"className":469,"style":444},[212,150],[24,471,50],{"className":472},[113,157,150],[24,474,60],{"className":475},[113,157,150],[24,477],{"className":478,"style":479},[212],"margin-right:0.1667em;",[24,481,484,494,497,500,503,506,509,512,568,571,574,577,580,583,586,590],{"className":482},[483],"minner",[24,485,489],{"className":486,"style":488},[117,487],"delimcenter","top:0em;",[24,490,71],{"className":491},[492,493],"delimsizing","size2",[24,495,307],{"className":496,"style":451},[448,449,450],[24,498],{"className":499,"style":479},[212],[24,501,84],{"className":502},[113,157],[24,504,71],{"className":505},[117],[24,507,60],{"className":508},[113,157],[24,510,76],{"className":511},[208],[24,513,515,518],{"className":514},[113],[24,516,299],{"className":517},[113,157],[24,519,521],{"className":520},[414],[24,522,524],{"className":523},[125],[24,525,527],{"className":526},[130],[24,528,530],{"className":529,"style":424},[134],[24,531,532,535],{"style":427},[24,533],{"className":534,"style":431},[142],[24,536,538],{"className":537},[147,148,149,150],[24,539,541,544,547,550,553,556,559,562,565],{"className":540},[113,150],[24,542,307],{"className":543,"style":451},[448,449,450,150],[24,545],{"className":546,"style":444},[212,150],[24,548,67],{"className":549,"style":231},[113,157,150],[24,551,71],{"className":552},[117,150],[24,554,60],{"className":555},[113,157,150],[24,557,76],{"className":558},[208,150],[24,560],{"className":561,"style":444},[212,150],[24,563,50],{"className":564},[113,157,150],[24,566,60],{"className":567},[113,157,150],[24,569],{"className":570,"style":479},[212],[24,572,50],{"className":573},[113,157],[24,575,60],{"className":576},[113,157],[24,578],{"className":579,"style":213},[212],[24,581,64],{"className":582},[217],[24,584],{"className":585,"style":213},[212],[24,587,370],{"className":588,"style":589},[113,157],"margin-right:0.0715em;",[24,591,593],{"className":592,"style":488},[208,487],[24,594,76],{"className":595},[492,493],[10,597,599],{"id":598},"高阶线性ode求解方法","高阶线性ODE求解方法",[601,602,604],"h3",{"id":603},"齐次线性ode","齐次线性ODE",[15,606,607],{},[18,608,20],{},[15,610,611],{},[24,612,614,749],{"className":613},[27],[24,615,617],{"className":616},[31],[33,618,619],{"xmlns":35},[37,620,621,746],{},[40,622,623,632,654,656,670,704,706,709,711,717,731,733,740,742,744],{},[624,625,626,629],"msub",{},[48,627,628],{},"a",[48,630,631],{},"n",[43,633,634,644],{},[40,635,636,642],{},[295,637,638,640],{},[48,639,50],{},[48,641,631],{},[48,643,53],{},[40,645,646,648],{},[48,647,50],{},[295,649,650,652],{},[48,651,60],{},[48,653,631],{},[62,655,64],{},[624,657,658,660],{},[48,659,628],{},[40,661,662,664,666],{},[48,663,631],{},[62,665,304],{},[667,668,669],"mn",{},"1",[43,671,672,688],{},[40,673,674,686],{},[295,675,676,678],{},[48,677,50],{},[40,679,680,682,684],{},[48,681,631],{},[62,683,304],{},[667,685,669],{},[48,687,53],{},[40,689,690,692],{},[48,691,50],{},[295,693,694,696],{},[48,695,60],{},[40,697,698,700,702],{},[48,699,631],{},[62,701,304],{},[667,703,669],{},[62,705,64],{},[62,707,708],{},"⋯",[62,710,64],{},[624,712,713,715],{},[48,714,628],{},[667,716,669],{},[43,718,719,725],{},[40,720,721,723],{},[48,722,50],{},[48,724,53],{},[40,726,727,729],{},[48,728,50],{},[48,730,60],{},[62,732,64],{},[624,734,735,737],{},[48,736,628],{},[667,738,739],{},"0",[48,741,53],{},[62,743,81],{},[667,745,739],{},[92,747,748],{"encoding":94},"a_n \\frac{d^n y}{dx^n} + a_{n-1} \\frac{d^{n-1} y}{dx^{n-1}} + \\dots + a_1 \\frac{dy}{dx} + a_0 y = 0",[24,750,752,945,1159,1178,1307,1365],{"className":751,"ariaHidden":100},[99],[24,753,755,759,802,936,939,942],{"className":754},[104],[24,756],{"className":757,"style":758},[108],"height:1.3081em;vertical-align:-0.345em;",[24,760,762,765],{"className":761},[113],[24,763,628],{"className":764},[113,157],[24,766,768],{"className":767},[414],[24,769,771,793],{"className":770},[125,126],[24,772,774,790],{"className":773},[130],[24,775,778],{"className":776,"style":777},[134],"height:0.1514em;",[24,779,781,784],{"style":780},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[24,782],{"className":783,"style":431},[142],[24,785,787],{"className":786},[147,148,149,150],[24,788,631],{"className":789},[113,157,150],[24,791,195],{"className":792},[194],[24,794,796],{"className":795},[130],[24,797,800],{"className":798,"style":799},[134],"height:0.15em;",[24,801],{},[24,803,805,808,933],{"className":804},[113],[24,806],{"className":807},[117,118],[24,809,811],{"className":810},[43],[24,812,814,925],{"className":813},[125,126],[24,815,817,922],{"className":816},[130],[24,818,821,869,877],{"className":819,"style":820},[134],"height:0.9631em;",[24,822,823,826],{"style":138},[24,824],{"className":825,"style":143},[142],[24,827,829],{"className":828},[147,148,149,150],[24,830,832,835],{"className":831},[113,150],[24,833,50],{"className":834},[113,157,150],[24,836,838,841],{"className":837},[113,150],[24,839,60],{"className":840},[113,157,150],[24,842,844],{"className":843},[414],[24,845,847],{"className":846},[125],[24,848,850],{"className":849},[130],[24,851,854],{"className":852,"style":853},[134],"height:0.5935em;",[24,855,857,861],{"style":856},"top:-2.786em;margin-right:0.0714em;",[24,858],{"className":859,"style":860},[142],"height:2.5em;",[24,862,866],{"className":863},[147,864,865,150],"reset-size3","size1",[24,867,631],{"className":868},[113,157,150],[24,870,871,874],{"style":163},[24,872],{"className":873,"style":143},[142],[24,875],{"className":876,"style":171},[170],[24,878,879,882],{"style":174},[24,880],{"className":881,"style":143},[142],[24,883,885],{"className":884},[147,148,149,150],[24,886,888,919],{"className":887},[113,150],[24,889,891,894],{"className":890},[113,150],[24,892,50],{"className":893},[113,157,150],[24,895,897],{"className":896},[414],[24,898,900],{"className":899},[125],[24,901,903],{"className":902},[130],[24,904,907],{"className":905,"style":906},[134],"height:0.7385em;",[24,908,910,913],{"style":909},"top:-2.931em;margin-right:0.0714em;",[24,911],{"className":912,"style":860},[142],[24,914,916],{"className":915},[147,864,865,150],[24,917,631],{"className":918},[113,157,150],[24,920,53],{"className":921,"style":190},[113,157,150],[24,923,195],{"className":924},[194],[24,926,928],{"className":927},[130],[24,929,931],{"className":930,"style":202},[134],[24,932],{},[24,934],{"className":935},[208,118],[24,937],{"className":938,"style":213},[212],[24,940,64],{"className":941},[217],[24,943],{"className":944,"style":213},[212],[24,946,948,952,1003,1150,1153,1156],{"className":947},[104],[24,949],{"className":950,"style":951},[108],"height:1.415em;vertical-align:-0.345em;",[24,953,955,958],{"className":954},[113],[24,956,628],{"className":957},[113,157],[24,959,961],{"className":960},[414],[24,962,964,994],{"className":963},[125,126],[24,965,967,991],{"className":966},[130],[24,968,971],{"className":969,"style":970},[134],"height:0.3011em;",[24,972,973,976],{"style":780},[24,974],{"className":975,"style":431},[142],[24,977,979],{"className":978},[147,148,149,150],[24,980,982,985,988],{"className":981},[113,150],[24,983,631],{"className":984},[113,157,150],[24,986,304],{"className":987},[217,150],[24,989,669],{"className":990},[113,150],[24,992,195],{"className":993},[194],[24,995,997],{"className":996},[130],[24,998,1001],{"className":999,"style":1000},[134],"height:0.2083em;",[24,1002],{},[24,1004,1006,1009,1147],{"className":1005},[113],[24,1007],{"className":1008},[117,118],[24,1010,1012],{"className":1011},[43],[24,1013,1015,1139],{"className":1014},[125,126],[24,1016,1018,1136],{"className":1017},[130],[24,1019,1022,1075,1083],{"className":1020,"style":1021},[134],"height:1.07em;",[24,1023,1024,1027],{"style":138},[24,1025],{"className":1026,"style":143},[142],[24,1028,1030],{"className":1029},[147,148,149,150],[24,1031,1033,1036],{"className":1032},[113,150],[24,1034,50],{"className":1035},[113,157,150],[24,1037,1039,1042],{"className":1038},[113,150],[24,1040,60],{"className":1041},[113,157,150],[24,1043,1045],{"className":1044},[414],[24,1046,1048],{"className":1047},[125],[24,1049,1051],{"className":1050},[130],[24,1052,1055],{"className":1053,"style":1054},[134],"height:0.7463em;",[24,1056,1057,1060],{"style":856},[24,1058],{"className":1059,"style":860},[142],[24,1061,1063],{"className":1062},[147,864,865,150],[24,1064,1066,1069,1072],{"className":1065},[113,150],[24,1067,631],{"className":1068},[113,157,150],[24,1070,304],{"className":1071},[217,150],[24,1073,669],{"className":1074},[113,150],[24,1076,1077,1080],{"style":163},[24,1078],{"className":1079,"style":143},[142],[24,1081],{"className":1082,"style":171},[170],[24,1084,1085,1088],{"style":174},[24,1086],{"className":1087,"style":143},[142],[24,1089,1091],{"className":1090},[147,148,149,150],[24,1092,1094,1133],{"className":1093},[113,150],[24,1095,1097,1100],{"className":1096},[113,150],[24,1098,50],{"className":1099},[113,157,150],[24,1101,1103],{"className":1102},[414],[24,1104,1106],{"className":1105},[125],[24,1107,1109],{"className":1108},[130],[24,1110,1113],{"className":1111,"style":1112},[134],"height:0.8913em;",[24,1114,1115,1118],{"style":909},[24,1116],{"className":1117,"style":860},[142],[24,1119,1121],{"className":1120},[147,864,865,150],[24,1122,1124,1127,1130],{"className":1123},[113,150],[24,1125,631],{"className":1126},[113,157,150],[24,1128,304],{"className":1129},[217,150],[24,1131,669],{"className":1132},[113,150],[24,1134,53],{"className":1135,"style":190},[113,157,150],[24,1137,195],{"className":1138},[194],[24,1140,1142],{"className":1141},[130],[24,1143,1145],{"className":1144,"style":202},[134],[24,1146],{},[24,1148],{"className":1149},[208,118],[24,1151],{"className":1152,"style":213},[212],[24,1154,64],{"className":1155},[217],[24,1157],{"className":1158,"style":213},[212],[24,1160,1162,1166,1169,1172,1175],{"className":1161},[104],[24,1163],{"className":1164,"style":1165},[108],"height:0.6667em;vertical-align:-0.0833em;",[24,1167,708],{"className":1168},[483],[24,1170],{"className":1171,"style":213},[212],[24,1173,64],{"className":1174},[217],[24,1176],{"className":1177,"style":213},[212],[24,1179,1181,1184,1224,1298,1301,1304],{"className":1180},[104],[24,1182],{"className":1183,"style":109},[108],[24,1185,1187,1190],{"className":1186},[113],[24,1188,628],{"className":1189},[113,157],[24,1191,1193],{"className":1192},[414],[24,1194,1196,1216],{"className":1195},[125,126],[24,1197,1199,1213],{"className":1198},[130],[24,1200,1202],{"className":1201,"style":970},[134],[24,1203,1204,1207],{"style":780},[24,1205],{"className":1206,"style":431},[142],[24,1208,1210],{"className":1209},[147,148,149,150],[24,1211,669],{"className":1212},[113,150],[24,1214,195],{"className":1215},[194],[24,1217,1219],{"className":1218},[130],[24,1220,1222],{"className":1221,"style":799},[134],[24,1223],{},[24,1225,1227,1230,1295],{"className":1226},[113],[24,1228],{"className":1229},[117,118],[24,1231,1233],{"className":1232},[43],[24,1234,1236,1287],{"className":1235},[125,126],[24,1237,1239,1284],{"className":1238},[130],[24,1240,1242,1259,1267],{"className":1241,"style":135},[134],[24,1243,1244,1247],{"style":138},[24,1245],{"className":1246,"style":143},[142],[24,1248,1250],{"className":1249},[147,148,149,150],[24,1251,1253,1256],{"className":1252},[113,150],[24,1254,50],{"className":1255},[113,157,150],[24,1257,60],{"className":1258},[113,157,150],[24,1260,1261,1264],{"style":163},[24,1262],{"className":1263,"style":143},[142],[24,1265],{"className":1266,"style":171},[170],[24,1268,1269,1272],{"style":174},[24,1270],{"className":1271,"style":143},[142],[24,1273,1275],{"className":1274},[147,148,149,150],[24,1276,1278,1281],{"className":1277},[113,150],[24,1279,50],{"className":1280},[113,157,150],[24,1282,53],{"className":1283,"style":190},[113,157,150],[24,1285,195],{"className":1286},[194],[24,1288,1290],{"className":1289},[130],[24,1291,1293],{"className":1292,"style":202},[134],[24,1294],{},[24,1296],{"className":1297},[208,118],[24,1299],{"className":1300,"style":213},[212],[24,1302,64],{"className":1303},[217],[24,1305],{"className":1306,"style":213},[212],[24,1308,1310,1313,1353,1356,1359,1362],{"className":1309},[104],[24,1311],{"className":1312,"style":385},[108],[24,1314,1316,1319],{"className":1315},[113],[24,1317,628],{"className":1318},[113,157],[24,1320,1322],{"className":1321},[414],[24,1323,1325,1345],{"className":1324},[125,126],[24,1326,1328,1342],{"className":1327},[130],[24,1329,1331],{"className":1330,"style":970},[134],[24,1332,1333,1336],{"style":780},[24,1334],{"className":1335,"style":431},[142],[24,1337,1339],{"className":1338},[147,148,149,150],[24,1340,739],{"className":1341},[113,150],[24,1343,195],{"className":1344},[194],[24,1346,1348],{"className":1347},[130],[24,1349,1351],{"className":1350,"style":799},[134],[24,1352],{},[24,1354,53],{"className":1355,"style":190},[113,157],[24,1357],{"className":1358,"style":247},[212],[24,1360,81],{"className":1361},[251],[24,1363],{"className":1364,"style":247},[212],[24,1366,1368,1372],{"className":1367},[104],[24,1369],{"className":1370,"style":1371},[108],"height:0.6444em;",[24,1373,739],{"className":1374},[113],[15,1376,1377],{},[18,1378,1379],{},"求解步骤：",[1381,1382,1383,1804,2010,3814],"ol",{},[1384,1385,1386,1387,1390],"li",{},"写出特征方程：",[1388,1389],"br",{},[24,1391,1393,1470],{"className":1392},[27],[24,1394,1396],{"className":1395},[31],[33,1397,1398],{"xmlns":35},[37,1399,1400,1467],{},[40,1401,1402,1408,1415,1417,1429,1441,1443,1445,1447,1453,1455,1457,1463,1465],{},[624,1403,1404,1406],{},[48,1405,628],{},[48,1407,631],{},[295,1409,1410,1413],{},[48,1411,1412],{},"λ",[48,1414,631],{},[62,1416,64],{},[624,1418,1419,1421],{},[48,1420,628],{},[40,1422,1423,1425,1427],{},[48,1424,631],{},[62,1426,304],{},[667,1428,669],{},[295,1430,1431,1433],{},[48,1432,1412],{},[40,1434,1435,1437,1439],{},[48,1436,631],{},[62,1438,304],{},[667,1440,669],{},[62,1442,64],{},[62,1444,708],{},[62,1446,64],{},[624,1448,1449,1451],{},[48,1450,628],{},[667,1452,669],{},[48,1454,1412],{},[62,1456,64],{},[624,1458,1459,1461],{},[48,1460,628],{},[667,1462,739],{},[62,1464,81],{},[667,1466,739],{},[92,1468,1469],{"encoding":94},"a_n \\lambda^n + a_{n-1} \\lambda^{n-1} + \\dots + a_1 \\lambda + a_0 = 0",[24,1471,1473,1559,1663,1681,1739,1795],{"className":1472,"ariaHidden":100},[99],[24,1474,1476,1480,1520,1550,1553,1556],{"className":1475},[104],[24,1477],{"className":1478,"style":1479},[108],"height:0.8444em;vertical-align:-0.15em;",[24,1481,1483,1486],{"className":1482},[113],[24,1484,628],{"className":1485},[113,157],[24,1487,1489],{"className":1488},[414],[24,1490,1492,1512],{"className":1491},[125,126],[24,1493,1495,1509],{"className":1494},[130],[24,1496,1498],{"className":1497,"style":777},[134],[24,1499,1500,1503],{"style":780},[24,1501],{"className":1502,"style":431},[142],[24,1504,1506],{"className":1505},[147,148,149,150],[24,1507,631],{"className":1508},[113,157,150],[24,1510,195],{"className":1511},[194],[24,1513,1515],{"className":1514},[130],[24,1516,1518],{"className":1517,"style":799},[134],[24,1519],{},[24,1521,1523,1526],{"className":1522},[113],[24,1524,1412],{"className":1525},[113,157],[24,1527,1529],{"className":1528},[414],[24,1530,1532],{"className":1531},[125],[24,1533,1535],{"className":1534},[130],[24,1536,1539],{"className":1537,"style":1538},[134],"height:0.6644em;",[24,1540,1541,1544],{"style":427},[24,1542],{"className":1543,"style":431},[142],[24,1545,1547],{"className":1546},[147,148,149,150],[24,1548,631],{"className":1549},[113,157,150],[24,1551],{"className":1552,"style":213},[212],[24,1554,64],{"className":1555},[217],[24,1557],{"className":1558,"style":213},[212],[24,1560,1562,1566,1615,1654,1657,1660],{"className":1561},[104],[24,1563],{"className":1564,"style":1565},[108],"height:1.0224em;vertical-align:-0.2083em;",[24,1567,1569,1572],{"className":1568},[113],[24,1570,628],{"className":1571},[113,157],[24,1573,1575],{"className":1574},[414],[24,1576,1578,1607],{"className":1577},[125,126],[24,1579,1581,1604],{"className":1580},[130],[24,1582,1584],{"className":1583,"style":970},[134],[24,1585,1586,1589],{"style":780},[24,1587],{"className":1588,"style":431},[142],[24,1590,1592],{"className":1591},[147,148,149,150],[24,1593,1595,1598,1601],{"className":1594},[113,150],[24,1596,631],{"className":1597},[113,157,150],[24,1599,304],{"className":1600},[217,150],[24,1602,669],{"className":1603},[113,150],[24,1605,195],{"className":1606},[194],[24,1608,1610],{"className":1609},[130],[24,1611,1613],{"className":1612,"style":1000},[134],[24,1614],{},[24,1616,1618,1621],{"className":1617},[113],[24,1619,1412],{"className":1620},[113,157],[24,1622,1624],{"className":1623},[414],[24,1625,1627],{"className":1626},[125],[24,1628,1630],{"className":1629},[130],[24,1631,1634],{"className":1632,"style":1633},[134],"height:0.8141em;",[24,1635,1636,1639],{"style":427},[24,1637],{"className":1638,"style":431},[142],[24,1640,1642],{"className":1641},[147,148,149,150],[24,1643,1645,1648,1651],{"className":1644},[113,150],[24,1646,631],{"className":1647},[113,157,150],[24,1649,304],{"className":1650},[217,150],[24,1652,669],{"className":1653},[113,150],[24,1655],{"className":1656,"style":213},[212],[24,1658,64],{"className":1659},[217],[24,1661],{"className":1662,"style":213},[212],[24,1664,1666,1669,1672,1675,1678],{"className":1665},[104],[24,1667],{"className":1668,"style":1165},[108],[24,1670,708],{"className":1671},[483],[24,1673],{"className":1674,"style":213},[212],[24,1676,64],{"className":1677},[217],[24,1679],{"className":1680,"style":213},[212],[24,1682,1684,1687,1727,1730,1733,1736],{"className":1683},[104],[24,1685],{"className":1686,"style":1479},[108],[24,1688,1690,1693],{"className":1689},[113],[24,1691,628],{"className":1692},[113,157],[24,1694,1696],{"className":1695},[414],[24,1697,1699,1719],{"className":1698},[125,126],[24,1700,1702,1716],{"className":1701},[130],[24,1703,1705],{"className":1704,"style":970},[134],[24,1706,1707,1710],{"style":780},[24,1708],{"className":1709,"style":431},[142],[24,1711,1713],{"className":1712},[147,148,149,150],[24,1714,669],{"className":1715},[113,150],[24,1717,195],{"className":1718},[194],[24,1720,1722],{"className":1721},[130],[24,1723,1725],{"className":1724,"style":799},[134],[24,1726],{},[24,1728,1412],{"className":1729},[113,157],[24,1731],{"className":1732,"style":213},[212],[24,1734,64],{"className":1735},[217],[24,1737],{"className":1738,"style":213},[212],[24,1740,1742,1746,1786,1789,1792],{"className":1741},[104],[24,1743],{"className":1744,"style":1745},[108],"height:0.5806em;vertical-align:-0.15em;",[24,1747,1749,1752],{"className":1748},[113],[24,1750,628],{"className":1751},[113,157],[24,1753,1755],{"className":1754},[414],[24,1756,1758,1778],{"className":1757},[125,126],[24,1759,1761,1775],{"className":1760},[130],[24,1762,1764],{"className":1763,"style":970},[134],[24,1765,1766,1769],{"style":780},[24,1767],{"className":1768,"style":431},[142],[24,1770,1772],{"className":1771},[147,148,149,150],[24,1773,739],{"className":1774},[113,150],[24,1776,195],{"className":1777},[194],[24,1779,1781],{"className":1780},[130],[24,1782,1784],{"className":1783,"style":799},[134],[24,1785],{},[24,1787],{"className":1788,"style":247},[212],[24,1790,81],{"className":1791},[251],[24,1793],{"className":1794,"style":247},[212],[24,1796,1798,1801],{"className":1797},[104],[24,1799],{"className":1800,"style":1371},[108],[24,1802,739],{"className":1803},[113],[1384,1805,1806,1807,2009],{},"求解得到特征根",[24,1808,1810,1852],{"className":1809},[27],[24,1811,1813],{"className":1812},[31],[33,1814,1815],{"xmlns":35},[37,1816,1817,1849],{},[40,1818,1819,1825,1828,1835,1837,1840,1842],{},[624,1820,1821,1823],{},[48,1822,1412],{},[667,1824,669],{},[62,1826,1827],{"separator":100},",",[624,1829,1830,1832],{},[48,1831,1412],{},[667,1833,1834],{},"2",[62,1836,1827],{"separator":100},[62,1838,1839],{},"…",[62,1841,1827],{"separator":100},[624,1843,1844,1846],{},[48,1845,1412],{},[48,1847,1848],{},"k",[92,1850,1851],{"encoding":94},"\\lambda_1, \\lambda_2, \\dots, \\lambda_k",[24,1853,1855],{"className":1854,"ariaHidden":100},[99],[24,1856,1858,1862,1902,1906,1909,1949,1952,1955,1958,1961,1964,1967],{"className":1857},[104],[24,1859],{"className":1860,"style":1861},[108],"height:0.8889em;vertical-align:-0.1944em;",[24,1863,1865,1868],{"className":1864},[113],[24,1866,1412],{"className":1867},[113,157],[24,1869,1871],{"className":1870},[414],[24,1872,1874,1894],{"className":1873},[125,126],[24,1875,1877,1891],{"className":1876},[130],[24,1878,1880],{"className":1879,"style":970},[134],[24,1881,1882,1885],{"style":780},[24,1883],{"className":1884,"style":431},[142],[24,1886,1888],{"className":1887},[147,148,149,150],[24,1889,669],{"className":1890},[113,150],[24,1892,195],{"className":1893},[194],[24,1895,1897],{"className":1896},[130],[24,1898,1900],{"className":1899,"style":799},[134],[24,1901],{},[24,1903,1827],{"className":1904},[1905],"mpunct",[24,1907],{"className":1908,"style":479},[212],[24,1910,1912,1915],{"className":1911},[113],[24,1913,1412],{"className":1914},[113,157],[24,1916,1918],{"className":1917},[414],[24,1919,1921,1941],{"className":1920},[125,126],[24,1922,1924,1938],{"className":1923},[130],[24,1925,1927],{"className":1926,"style":970},[134],[24,1928,1929,1932],{"style":780},[24,1930],{"className":1931,"style":431},[142],[24,1933,1935],{"className":1934},[147,148,149,150],[24,1936,1834],{"className":1937},[113,150],[24,1939,195],{"className":1940},[194],[24,1942,1944],{"className":1943},[130],[24,1945,1947],{"className":1946,"style":799},[134],[24,1948],{},[24,1950,1827],{"className":1951},[1905],[24,1953],{"className":1954,"style":479},[212],[24,1956,1839],{"className":1957},[483],[24,1959],{"className":1960,"style":479},[212],[24,1962,1827],{"className":1963},[1905],[24,1965],{"className":1966,"style":479},[212],[24,1968,1970,1973],{"className":1969},[113],[24,1971,1412],{"className":1972},[113,157],[24,1974,1976],{"className":1975},[414],[24,1977,1979,2001],{"className":1978},[125,126],[24,1980,1982,1998],{"className":1981},[130],[24,1983,1986],{"className":1984,"style":1985},[134],"height:0.3361em;",[24,1987,1988,1991],{"style":780},[24,1989],{"className":1990,"style":431},[142],[24,1992,1994],{"className":1993},[147,148,149,150],[24,1995,1848],{"className":1996,"style":1997},[113,157,150],"margin-right:0.0315em;",[24,1999,195],{"className":2000},[194],[24,2002,2004],{"className":2003},[130],[24,2005,2007],{"className":2006,"style":799},[134],[24,2008],{},"。",[1384,2011,2012,2013],{},"根据特征根的类型构建通解：",[2014,2015,2016,2206,2679,2913,3364],"ul",{},[1384,2017,2018,2019,2091,2092],{},"单实根 ",[24,2020,2022,2041],{"className":2021},[27],[24,2023,2025],{"className":2024},[31],[33,2026,2027],{"xmlns":35},[37,2028,2029,2038],{},[40,2030,2031],{},[624,2032,2033,2035],{},[48,2034,1412],{},[48,2036,2037],{},"i",[92,2039,2040],{"encoding":94},"\\lambda_i",[24,2042,2044],{"className":2043,"ariaHidden":100},[99],[24,2045,2047,2050],{"className":2046},[104],[24,2048],{"className":2049,"style":1479},[108],[24,2051,2053,2056],{"className":2052},[113],[24,2054,1412],{"className":2055},[113,157],[24,2057,2059],{"className":2058},[414],[24,2060,2062,2083],{"className":2061},[125,126],[24,2063,2065,2080],{"className":2064},[130],[24,2066,2069],{"className":2067,"style":2068},[134],"height:0.3117em;",[24,2070,2071,2074],{"style":780},[24,2072],{"className":2073,"style":431},[142],[24,2075,2077],{"className":2076},[147,148,149,150],[24,2078,2037],{"className":2079},[113,157,150],[24,2081,195],{"className":2082},[194],[24,2084,2086],{"className":2085},[130],[24,2087,2089],{"className":2088,"style":799},[134],[24,2090],{},"：对应解为 ",[24,2093,2095,2121],{"className":2094},[27],[24,2096,2098],{"className":2097},[31],[33,2099,2100],{"xmlns":35},[37,2101,2102,2118],{},[40,2103,2104],{},[295,2105,2106,2108],{},[48,2107,299],{},[40,2109,2110,2116],{},[624,2111,2112,2114],{},[48,2113,1412],{},[48,2115,2037],{},[48,2117,60],{},[92,2119,2120],{"encoding":94},"e^{\\lambda_i x}",[24,2122,2124],{"className":2123,"ariaHidden":100},[99],[24,2125,2127,2131],{"className":2126},[104],[24,2128],{"className":2129,"style":2130},[108],"height:0.8491em;",[24,2132,2134,2137],{"className":2133},[113],[24,2135,299],{"className":2136},[113,157],[24,2138,2140],{"className":2139},[414],[24,2141,2143],{"className":2142},[125],[24,2144,2146],{"className":2145},[130],[24,2147,2149],{"className":2148,"style":2130},[134],[24,2150,2151,2154],{"style":427},[24,2152],{"className":2153,"style":431},[142],[24,2155,2157],{"className":2156},[147,148,149,150],[24,2158,2160,2203],{"className":2159},[113,150],[24,2161,2163,2166],{"className":2162},[113,150],[24,2164,1412],{"className":2165},[113,157,150],[24,2167,2169],{"className":2168},[414],[24,2170,2172,2194],{"className":2171},[125,126],[24,2173,2175,2191],{"className":2174},[130],[24,2176,2179],{"className":2177,"style":2178},[134],"height:0.3281em;",[24,2180,2182,2185],{"style":2181},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[24,2183],{"className":2184,"style":860},[142],[24,2186,2188],{"className":2187},[147,864,865,150],[24,2189,2037],{"className":2190},[113,157,150],[24,2192,195],{"className":2193},[194],[24,2195,2197],{"className":2196},[130],[24,2198,2201],{"className":2199,"style":2200},[134],"height:0.143em;",[24,2202],{},[24,2204,60],{"className":2205},[113,157,150],[1384,2207,2208,2237,2238,2091,2307],{},[24,2209,2211,2224],{"className":2210},[27],[24,2212,2214],{"className":2213},[31],[33,2215,2216],{"xmlns":35},[37,2217,2218,2222],{},[40,2219,2220],{},[48,2221,1848],{},[92,2223,1848],{"encoding":94},[24,2225,2227],{"className":2226,"ariaHidden":100},[99],[24,2228,2230,2234],{"className":2229},[104],[24,2231],{"className":2232,"style":2233},[108],"height:0.6944em;",[24,2235,1848],{"className":2236,"style":1997},[113,157]," 重实根 ",[24,2239,2241,2258],{"className":2240},[27],[24,2242,2244],{"className":2243},[31],[33,2245,2246],{"xmlns":35},[37,2247,2248,2256],{},[40,2249,2250],{},[624,2251,2252,2254],{},[48,2253,1412],{},[48,2255,2037],{},[92,2257,2040],{"encoding":94},[24,2259,2261],{"className":2260,"ariaHidden":100},[99],[24,2262,2264,2267],{"className":2263},[104],[24,2265],{"className":2266,"style":1479},[108],[24,2268,2270,2273],{"className":2269},[113],[24,2271,1412],{"className":2272},[113,157],[24,2274,2276],{"className":2275},[414],[24,2277,2279,2299],{"className":2278},[125,126],[24,2280,2282,2296],{"className":2281},[130],[24,2283,2285],{"className":2284,"style":2068},[134],[24,2286,2287,2290],{"style":780},[24,2288],{"className":2289,"style":431},[142],[24,2291,2293],{"className":2292},[147,148,149,150],[24,2294,2037],{"className":2295},[113,157,150],[24,2297,195],{"className":2298},[194],[24,2300,2302],{"className":2301},[130],[24,2303,2305],{"className":2304,"style":799},[134],[24,2306],{},[24,2308,2310,2380],{"className":2309},[27],[24,2311,2313],{"className":2312},[31],[33,2314,2315],{"xmlns":35},[37,2316,2317,2377],{},[40,2318,2319,2321,2327,2329,2335,2337,2339,2341,2343,2349,2361,2363],{},[62,2320,71],{"stretchy":70},[624,2322,2323,2325],{},[48,2324,370],{},[667,2326,669],{},[62,2328,64],{},[624,2330,2331,2333],{},[48,2332,370],{},[667,2334,1834],{},[48,2336,60],{},[62,2338,64],{},[62,2340,708],{},[62,2342,64],{},[624,2344,2345,2347],{},[48,2346,370],{},[48,2348,1848],{},[295,2350,2351,2353],{},[48,2352,60],{},[40,2354,2355,2357,2359],{},[48,2356,1848],{},[62,2358,304],{},[667,2360,669],{},[62,2362,76],{"stretchy":70},[295,2364,2365,2367],{},[48,2366,299],{},[40,2368,2369,2375],{},[624,2370,2371,2373],{},[48,2372,1412],{},[48,2374,2037],{},[48,2376,60],{},[92,2378,2379],{"encoding":94},"(C_1 + C_2 x + \\dots + C_k x^{k-1}) e^{\\lambda_i x}",[24,2381,2383,2442,2501,2519],{"className":2382,"ariaHidden":100},[99],[24,2384,2386,2389,2392,2433,2436,2439],{"className":2385},[104],[24,2387],{"className":2388,"style":227},[108],[24,2390,71],{"className":2391},[117],[24,2393,2395,2398],{"className":2394},[113],[24,2396,370],{"className":2397,"style":589},[113,157],[24,2399,2401],{"className":2400},[414],[24,2402,2404,2425],{"className":2403},[125,126],[24,2405,2407,2422],{"className":2406},[130],[24,2408,2410],{"className":2409,"style":970},[134],[24,2411,2413,2416],{"style":2412},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[24,2414],{"className":2415,"style":431},[142],[24,2417,2419],{"className":2418},[147,148,149,150],[24,2420,669],{"className":2421},[113,150],[24,2423,195],{"className":2424},[194],[24,2426,2428],{"className":2427},[130],[24,2429,2431],{"className":2430,"style":799},[134],[24,2432],{},[24,2434],{"className":2435,"style":213},[212],[24,2437,64],{"className":2438},[217],[24,2440],{"className":2441,"style":213},[212],[24,2443,2445,2449,2489,2492,2495,2498],{"className":2444},[104],[24,2446],{"className":2447,"style":2448},[108],"height:0.8333em;vertical-align:-0.15em;",[24,2450,2452,2455],{"className":2451},[113],[24,2453,370],{"className":2454,"style":589},[113,157],[24,2456,2458],{"className":2457},[414],[24,2459,2461,2481],{"className":2460},[125,126],[24,2462,2464,2478],{"className":2463},[130],[24,2465,2467],{"className":2466,"style":970},[134],[24,2468,2469,2472],{"style":2412},[24,2470],{"className":2471,"style":431},[142],[24,2473,2475],{"className":2474},[147,148,149,150],[24,2476,1834],{"className":2477},[113,150],[24,2479,195],{"className":2480},[194],[24,2482,2484],{"className":2483},[130],[24,2485,2487],{"className":2486,"style":799},[134],[24,2488],{},[24,2490,60],{"className":2491},[113,157],[24,2493],{"className":2494,"style":213},[212],[24,2496,64],{"className":2497},[217],[24,2499],{"className":2500,"style":213},[212],[24,2502,2504,2507,2510,2513,2516],{"className":2503},[104],[24,2505],{"className":2506,"style":1165},[108],[24,2508,708],{"className":2509},[483],[24,2511],{"className":2512,"style":213},[212],[24,2514,64],{"className":2515},[217],[24,2517],{"className":2518,"style":213},[212],[24,2520,2522,2526,2566,2604,2607],{"className":2521},[104],[24,2523],{"className":2524,"style":2525},[108],"height:1.0991em;vertical-align:-0.25em;",[24,2527,2529,2532],{"className":2528},[113],[24,2530,370],{"className":2531,"style":589},[113,157],[24,2533,2535],{"className":2534},[414],[24,2536,2538,2558],{"className":2537},[125,126],[24,2539,2541,2555],{"className":2540},[130],[24,2542,2544],{"className":2543,"style":1985},[134],[24,2545,2546,2549],{"style":2412},[24,2547],{"className":2548,"style":431},[142],[24,2550,2552],{"className":2551},[147,148,149,150],[24,2553,1848],{"className":2554,"style":1997},[113,157,150],[24,2556,195],{"className":2557},[194],[24,2559,2561],{"className":2560},[130],[24,2562,2564],{"className":2563,"style":799},[134],[24,2565],{},[24,2567,2569,2572],{"className":2568},[113],[24,2570,60],{"className":2571},[113,157],[24,2573,2575],{"className":2574},[414],[24,2576,2578],{"className":2577},[125],[24,2579,2581],{"className":2580},[130],[24,2582,2584],{"className":2583,"style":2130},[134],[24,2585,2586,2589],{"style":427},[24,2587],{"className":2588,"style":431},[142],[24,2590,2592],{"className":2591},[147,148,149,150],[24,2593,2595,2598,2601],{"className":2594},[113,150],[24,2596,1848],{"className":2597,"style":1997},[113,157,150],[24,2599,304],{"className":2600},[217,150],[24,2602,669],{"className":2603},[113,150],[24,2605,76],{"className":2606},[208],[24,2608,2610,2613],{"className":2609},[113],[24,2611,299],{"className":2612},[113,157],[24,2614,2616],{"className":2615},[414],[24,2617,2619],{"className":2618},[125],[24,2620,2622],{"className":2621},[130],[24,2623,2625],{"className":2624,"style":2130},[134],[24,2626,2627,2630],{"style":427},[24,2628],{"className":2629,"style":431},[142],[24,2631,2633],{"className":2632},[147,148,149,150],[24,2634,2636,2676],{"className":2635},[113,150],[24,2637,2639,2642],{"className":2638},[113,150],[24,2640,1412],{"className":2641},[113,157,150],[24,2643,2645],{"className":2644},[414],[24,2646,2648,2668],{"className":2647},[125,126],[24,2649,2651,2665],{"className":2650},[130],[24,2652,2654],{"className":2653,"style":2178},[134],[24,2655,2656,2659],{"style":2181},[24,2657],{"className":2658,"style":860},[142],[24,2660,2662],{"className":2661},[147,864,865,150],[24,2663,2037],{"className":2664},[113,157,150],[24,2666,195],{"className":2667},[194],[24,2669,2671],{"className":2670},[130],[24,2672,2674],{"className":2673,"style":2200},[134],[24,2675],{},[24,2677,60],{"className":2678},[113,157,150],[1384,2680,2681,2682,2710,2711,2091,2771],{},"对于",[24,2683,2685,2698],{"className":2684},[27],[24,2686,2688],{"className":2687},[31],[33,2689,2690],{"xmlns":35},[37,2691,2692,2696],{},[40,2693,2694],{},[48,2695,1848],{},[92,2697,1848],{"encoding":94},[24,2699,2701],{"className":2700,"ariaHidden":100},[99],[24,2702,2704,2707],{"className":2703},[104],[24,2705],{"className":2706,"style":2233},[108],[24,2708,1848],{"className":2709,"style":1997},[113,157],"重复根 ",[24,2712,2714,2736],{"className":2713},[27],[24,2715,2717],{"className":2716},[31],[33,2718,2719],{"xmlns":35},[37,2720,2721,2733],{},[40,2722,2723,2726,2728,2731],{},[48,2724,2725],{},"α",[62,2727,64],{},[48,2729,2730],{},"β",[48,2732,2037],{},[92,2734,2735],{"encoding":94},"\\alpha + \\beta i",[24,2737,2739,2758],{"className":2738,"ariaHidden":100},[99],[24,2740,2742,2745,2749,2752,2755],{"className":2741},[104],[24,2743],{"className":2744,"style":1165},[108],[24,2746,2725],{"className":2747,"style":2748},[113,157],"margin-right:0.0037em;",[24,2750],{"className":2751,"style":213},[212],[24,2753,64],{"className":2754},[217],[24,2756],{"className":2757,"style":213},[212],[24,2759,2761,2764,2768],{"className":2760},[104],[24,2762],{"className":2763,"style":1861},[108],[24,2765,2730],{"className":2766,"style":2767},[113,157],"margin-right:0.0528em;",[24,2769,2037],{"className":2770},[113,157],[24,2772,2774,2829],{"className":2773},[27],[24,2775,2777],{"className":2776},[31],[33,2778,2779],{"xmlns":35},[37,2780,2781,2826],{},[40,2782,2783,2793,2795,2798,2801,2803,2805,2807,2809,2811,2814,2816,2818,2820,2822,2824],{},[295,2784,2785,2787],{},[48,2786,299],{},[40,2788,2789,2791],{},[48,2790,2725],{},[48,2792,60],{},[62,2794,71],{"stretchy":70},[48,2796,2797],{},"cos",[62,2799,2800],{},"⁡",[62,2802,71],{"stretchy":70},[48,2804,2730],{},[48,2806,60],{},[62,2808,76],{"stretchy":70},[62,2810,1827],{"separator":100},[48,2812,2813],{},"sin",[62,2815,2800],{},[62,2817,71],{"stretchy":70},[48,2819,2730],{},[48,2821,60],{},[62,2823,76],{"stretchy":70},[62,2825,76],{"stretchy":70},[92,2827,2828],{"encoding":94},"e^{\\alpha x} (\\cos(\\beta x), \\sin(\\beta x))",[24,2830,2832],{"className":2831,"ariaHidden":100},[99],[24,2833,2835,2838,2873,2876,2879,2882,2885,2888,2891,2894,2897,2900,2903,2906,2909],{"className":2834},[104],[24,2836],{"className":2837,"style":227},[108],[24,2839,2841,2844],{"className":2840},[113],[24,2842,299],{"className":2843},[113,157],[24,2845,2847],{"className":2846},[414],[24,2848,2850],{"className":2849},[125],[24,2851,2853],{"className":2852},[130],[24,2854,2856],{"className":2855,"style":1538},[134],[24,2857,2858,2861],{"style":427},[24,2859],{"className":2860,"style":431},[142],[24,2862,2864],{"className":2863},[147,148,149,150],[24,2865,2867,2870],{"className":2866},[113,150],[24,2868,2725],{"className":2869,"style":2748},[113,157,150],[24,2871,60],{"className":2872},[113,157,150],[24,2874,71],{"className":2875},[117],[24,2877,2797],{"className":2878},[448],[24,2880,71],{"className":2881},[117],[24,2883,2730],{"className":2884,"style":2767},[113,157],[24,2886,60],{"className":2887},[113,157],[24,2889,76],{"className":2890},[208],[24,2892,1827],{"className":2893},[1905],[24,2895],{"className":2896,"style":479},[212],[24,2898,2813],{"className":2899},[448],[24,2901,71],{"className":2902},[117],[24,2904,2730],{"className":2905,"style":2767},[113,157],[24,2907,60],{"className":2908},[113,157],[24,2910,2912],{"className":2911},[208],"))",[1384,2914,2681,2915,2943,2944,2091,2999],{},[24,2916,2918,2931],{"className":2917},[27],[24,2919,2921],{"className":2920},[31],[33,2922,2923],{"xmlns":35},[37,2924,2925,2929],{},[40,2926,2927],{},[48,2928,1848],{},[92,2930,1848],{"encoding":94},[24,2932,2934],{"className":2933,"ariaHidden":100},[99],[24,2935,2937,2940],{"className":2936},[104],[24,2938],{"className":2939,"style":2233},[108],[24,2941,1848],{"className":2942,"style":1997},[113,157],"重复复根 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",[24,4832,4834,4888],{"className":4833},[27],[24,4835,4837],{"className":4836},[31],[33,4838,4839],{"xmlns":35},[37,4840,4841,4885],{},[40,4842,4843,4849,4851,4854,4860,4862,4865,4877,4879,4881,4883],{},[624,4844,4845,4847],{},[48,4846,53],{},[48,4848,15],{},[62,4850,81],{},[48,4852,4853],{},"A",[295,4855,4856,4858],{},[48,4857,60],{},[48,4859,631],{},[62,4861,64],{},[48,4863,4864],{},"B",[295,4866,4867,4869],{},[48,4868,60],{},[40,4870,4871,4873,4875],{},[48,4872,631],{},[62,4874,304],{},[667,4876,669],{},[62,4878,64],{},[62,4880,708],{},[62,4882,64],{},[48,4884,370],{},[92,4886,4887],{"encoding":94},"y_p = Ax^n + Bx^{n-1} + \\dots + C",[24,4889,4891,4946,4994,5052,5070],{"className":4890,"ariaHidden":100},[99],[24,4892,4894,4897,4937,4940,4943],{"className":4893},[104],[24,4895],{"className":4896,"style":4739},[108],[24,4898,4900,4903],{"className":4899},[113],[24,4901,53],{"className":4902,"style":190},[113,157],[24,4904,4906],{"className":4905},[414],[24,4907,4909,4929],{"className":4908},[125,126],[24,4910,4912,4926],{"className":4911},[130],[24,4913,4915],{"className":4914,"style":777},[134],[24,4916,4917,4920],{"style":4640},[24,4918],{"className":4919,"style":431},[142],[24,4921,4923],{"className":4922},[147,148,149,150],[24,4924,15],{"className":4925},[113,157,150],[24,4927,195],{"className":4928},[194],[24,4930,4932],{"className":4931},[130],[24,4933,4935],{"className":4934,"style":4778},[134],[24,4936],{},[24,4938],{"className":4939,"style":247},[212],[24,4941,81],{"className":4942},[251],[24,4944],{"className":4945,"style":247},[212],[24,4947,4949,4953,4956,4985,4988,4991],{"className":4948},[104],[24,4950],{"className":4951,"style":4952},[108],"height:0.7667em;vertical-align:-0.0833em;",[24,4954,4853],{"className":4955},[113,157],[24,4957,4959,4962],{"className":4958},[113],[24,4960,60],{"className":4961},[113,157],[24,4963,4965],{"className":4964},[414],[24,4966,4968],{"className":4967},[125],[24,4969,4971],{"className":4970},[130],[24,4972,4974],{"className":4973,"style":1538},[134],[24,4975,4976,4979],{"style":427},[24,4977],{"className":4978,"style":431},[142],[24,4980,4982],{"className":4981},[147,148,149,150],[24,4983,631],{"className":4984},[113,157,150],[24,4986],{"className":4987,"style":213},[212],[24,4989,64],{"className":4990},[217],[24,4992],{"className":4993,"style":213},[212],[24,4995,4997,5001,5005,5043,5046,5049],{"className":4996},[104],[24,4998],{"className":4999,"style":5000},[108],"height:0.8974em;vertical-align:-0.0833em;",[24,5002,4864],{"className":5003,"style":5004},[113,157],"margin-right:0.0502em;",[24,5006,5008,5011],{"className":5007},[113],[24,5009,60],{"className":5010},[113,157],[24,5012,5014],{"className":5013},[414],[24,5015,5017],{"className":5016},[125],[24,5018,5020],{"className":5019},[130],[24,5021,5023],{"className":5022,"style":1633},[134],[24,5024,5025,5028],{"style":427},[24,5026],{"className":5027,"style":431},[142],[24,5029,5031],{"className":5030},[147,148,149,150],[24,5032,5034,5037,5040],{"className":5033},[113,150],[24,5035,631],{"className":5036},[113,157,150],[24,5038,304],{"className":5039},[217,150],[24,5041,669],{"className":5042},[113,150],[24,5044],{"className":5045,"style":213},[212],[24,5047,64],{"className":5048},[217],[24,5050],{"className":5051,"style":213},[212],[24,5053,5055,5058,5061,5064,5067],{"className":5054},[104],[24,5056],{"className":5057,"style":1165},[108],[24,5059,708],{"className":5060},[483],[24,5062],{"className":5063,"style":213},[212],[24,5065,64],{"className":5066},[217],[24,5068],{"className":5069,"style":213},[212],[24,5071,5073,5077],{"className":5072},[104],[24,5074],{"className":5075,"style":5076},[108],"height:0.6833em;",[24,5078,370],{"className":5079,"style":589},[113,157]," 的形式。",[1384,5082,4786,5083,5126,5127,5080],{},[24,5084,5086,5105],{"className":5085},[27],[24,5087,5089],{"className":5088},[31],[33,5090,5091],{"xmlns":35},[37,5092,5093,5103],{},[40,5094,5095,5097,5099,5101],{},[48,5096,3955],{},[62,5098,71],{"stretchy":70},[48,5100,60],{},[62,5102,76],{"stretchy":70},[92,5104,4686],{"encoding":94},[24,5106,5108],{"className":5107,"ariaHidden":100},[99],[24,5109,5111,5114,5117,5120,5123],{"className":5110},[104],[24,5112],{"className":5113,"style":227},[108],[24,5115,3955],{"className":5116,"style":190},[113,157],[24,5118,71],{"className":5119},[117],[24,5121,60],{"className":5122},[113,157],[24,5124,76],{"className":5125},[208]," 是指数函数，尝试 ",[24,5128,5130,5162],{"className":5129},[27],[24,5131,5133],{"className":5132},[31],[33,5134,5135],{"xmlns":35},[37,5136,5137,5159],{},[40,5138,5139,5145,5147,5149],{},[624,5140,5141,5143],{},[48,5142,53],{},[48,5144,15],{},[62,5146,81],{},[48,5148,4853],{},[295,5150,5151,5153],{},[48,5152,299],{},[40,5154,5155,5157],{},[48,5156,1848],{},[48,5158,60],{},[92,5160,5161],{"encoding":94},"y_p = Ae^{kx}",[24,5163,5165,5220],{"className":5164,"ariaHidden":100},[99],[24,5166,5168,5171,5211,5214,5217],{"className":5167},[104],[24,5169],{"className":5170,"style":4739},[108],[24,5172,5174,5177],{"className":5173},[113],[24,5175,53],{"className":5176,"style":190},[113,157],[24,5178,5180],{"className":5179},[414],[24,5181,5183,5203],{"className":5182},[125,126],[24,5184,5186,5200],{"className":5185},[130],[24,5187,5189],{"className":5188,"style":777},[134],[24,5190,5191,5194],{"style":4640},[24,5192],{"className":5193,"style":431},[142],[24,5195,5197],{"className":5196},[147,148,149,150],[24,5198,15],{"className":5199},[113,157,150],[24,5201,195],{"className":5202},[194],[24,5204,5206],{"className":5205},[130],[24,5207,5209],{"className":5208,"style":4778},[134],[24,5210],{},[24,5212],{"className":5213,"style":247},[212],[24,5215,81],{"className":5216},[251],[24,5218],{"className":5219,"style":247},[212],[24,5221,5223,5226,5229],{"className":5222},[104],[24,5224],{"className":5225,"style":2130},[108],[24,5227,4853],{"className":5228},[113,157],[24,5230,5232,5235],{"className":5231},[113],[24,5233,299],{"className":5234},[113,157],[24,5236,5238],{"className":5237},[414],[24,5239,5241],{"className":5240},[125],[24,5242,5244],{"className":5243},[130],[24,5245,5247],{"className":5246,"style":2130},[134],[24,5248,5249,5252],{"style":427},[24,5250],{"className":5251,"style":431},[142],[24,5253,5255],{"className":5254},[147,148,149,150],[24,5256,5258,5261],{"className":5257},[113,150],[24,5259,1848],{"className":5260,"style":1997},[113,157,150],[24,5262,60],{"className":5263},[113,157,150],[1384,5265,4786,5266,5309,5310,5080],{},[24,5267,5269,5288],{"className":5268},[27],[24,5270,5272],{"className":5271},[31],[33,5273,5274],{"xmlns":35},[37,5275,5276,5286],{},[40,5277,5278,5280,5282,5284],{},[48,5279,3955],{},[62,5281,71],{"stretchy":70},[48,5283,60],{},[62,5285,76],{"stretchy":70},[92,5287,4686],{"encoding":94},[24,5289,5291],{"className":5290,"ariaHidden":100},[99],[24,5292,5294,5297,5300,5303,5306],{"className":5293},[104],[24,5295],{"className":5296,"style":227},[108],[24,5298,3955],{"className":5299,"style":190},[113,157],[24,5301,71],{"className":5302},[117],[24,5304,60],{"className":5305},[113,157],[24,5307,76],{"className":5308},[208]," 是三角函数，尝试 ",[24,5311,5313,5363],{"className":5312},[27],[24,5314,5316],{"className":5315},[31],[33,5317,5318],{"xmlns":35},[37,5319,5320,5360],{},[40,5321,5322,5328,5330,5332,5334,5336,5338,5340,5342,5344,5346,5348,5350,5352,5354,5356,5358],{},[624,5323,5324,5326],{},[48,5325,53],{},[48,5327,15],{},[62,5329,81],{},[48,5331,4853],{},[48,5333,2797],{},[62,5335,2800],{},[62,5337,71],{"stretchy":70},[48,5339,1848],{},[48,5341,60],{},[62,5343,76],{"stretchy":70},[62,5345,64],{},[48,5347,4864],{},[48,5349,2813],{},[62,5351,2800],{},[62,5353,71],{"stretchy":70},[48,5355,1848],{},[48,5357,60],{},[62,5359,76],{"stretchy":70},[92,5361,5362],{"encoding":94},"y_p = A\\cos(kx) + B\\sin(kx)",[24,5364,5366,5421,5457],{"className":5365,"ariaHidden":100},[99],[24,5367,5369,5372,5412,5415,5418],{"className":5368},[104],[24,5370],{"className":5371,"style":4739},[108],[24,5373,5375,5378],{"className":5374},[113],[24,5376,53],{"className":5377,"style":190},[113,157],[24,5379,5381],{"className":5380},[414],[24,5382,5384,5404],{"className":5383},[125,126],[24,5385,5387,5401],{"className":5386},[130],[24,5388,5390],{"className":5389,"style":777},[134],[24,5391,5392,5395],{"style":4640},[24,5393],{"className":5394,"style":431},[142],[24,5396,5398],{"className":5397},[147,148,149,150],[24,5399,15],{"className":5400},[113,157,150],[24,5402,195],{"className":5403},[194],[24,5405,5407],{"className":5406},[130],[24,5408,5410],{"className":5409,"style":4778},[134],[24,5411],{},[24,5413],{"className":5414,"style":247},[212],[24,5416,81],{"className":5417},[251],[24,5419],{"className":5420,"style":247},[212],[24,5422,5424,5427,5430,5433,5436,5439,5442,5445,5448,5451,5454],{"className":5423},[104],[24,5425],{"className":5426,"style":227},[108],[24,5428,4853],{"className":5429},[113,157],[24,5431],{"className":5432,"style":479},[212],[24,5434,2797],{"className":5435},[448],[24,5437,71],{"className":5438},[117],[24,5440,1848],{"className":5441,"style":1997},[113,157],[24,5443,60],{"className":5444},[113,157],[24,5446,76],{"className":5447},[208],[24,5449],{"className":5450,"style":213},[212],[24,5452,64],{"className":5453},[217],[24,5455],{"className":5456,"style":213},[212],[24,5458,5460,5463,5466,5469,5472,5475,5478,5481],{"className":5459},[104],[24,5461],{"className":5462,"style":227},[108],[24,5464,4864],{"className":5465,"style":5004},[113,157],[24,5467],{"className":5468,"style":479},[212],[24,5470,2813],{"className":5471},[448],[24,5473,71],{"className":5474},[117],[24,5476,1848],{"className":5477,"style":1997},[113,157],[24,5479,60],{"className":5480},[113,157],[24,5482,76],{"className":5483},[208],[1384,5485,5486,5487,5556],{},"将 ",[24,5488,5490,5507],{"className":5489},[27],[24,5491,5493],{"className":5492},[31],[33,5494,5495],{"xmlns":35},[37,5496,5497,5505],{},[40,5498,5499],{},[624,5500,5501,5503],{},[48,5502,53],{},[48,5504,15],{},[92,5506,4729],{"encoding":94},[24,5508,5510],{"className":5509,"ariaHidden":100},[99],[24,5511,5513,5516],{"className":5512},[104],[24,5514],{"className":5515,"style":4739},[108],[24,5517,5519,5522],{"className":5518},[113],[24,5520,53],{"className":5521,"style":190},[113,157],[24,5523,5525],{"className":5524},[414],[24,5526,5528,5548],{"className":5527},[125,126],[24,5529,5531,5545],{"className":5530},[130],[24,5532,5534],{"className":5533,"style":777},[134],[24,5535,5536,5539],{"style":4640},[24,5537],{"className":5538,"style":431},[142],[24,5540,5542],{"className":5541},[147,148,149,150],[24,5543,15],{"className":5544},[113,157,150],[24,5546,195],{"className":5547},[194],[24,5549,5551],{"className":5550},[130],[24,5552,5554],{"className":5553,"style":4778},[134],[24,5555],{}," 代入原方程，求解系数。",[1384,5558,5559,5560],{},"最终通解为 ",[24,5561,5563,5593],{"className":5562},[27],[24,5564,5566],{"className":5565},[31],[33,5567,5568],{"xmlns":35},[37,5569,5570,5590],{},[40,5571,5572,5574,5576,5582,5584],{},[48,5573,53],{},[62,5575,81],{},[624,5577,5578,5580],{},[48,5579,53],{},[48,5581,4607],{},[62,5583,64],{},[624,5585,5586,5588],{},[48,5587,53],{},[48,5589,15],{},[92,5591,5592],{"encoding":94},"y = y_h + y_p",[24,5594,5596,5614,5670],{"className":5595,"ariaHidden":100},[99],[24,5597,5599,5602,5605,5608,5611],{"className":5598},[104],[24,5600],{"className":5601,"style":385},[108],[24,5603,53],{"className":5604,"style":190},[113,157],[24,5606],{"className":5607,"style":247},[212],[24,5609,81],{"className":5610},[251],[24,5612],{"className":5613,"style":247},[212],[24,5615,5617,5621,5661,5664,5667],{"className":5616},[104],[24,5618],{"className":5619,"style":5620},[108],"height:0.7778em;vertical-align:-0.1944em;",[24,5622,5624,5627],{"className":5623},[113],[24,5625,53],{"className":5626,"style":190},[113,157],[24,5628,5630],{"className":5629},[414],[24,5631,5633,5653],{"className":5632},[125,126],[24,5634,5636,5650],{"className":5635},[130],[24,5637,5639],{"className":5638,"style":1985},[134],[24,5640,5641,5644],{"style":4640},[24,5642],{"className":5643,"style":431},[142],[24,5645,5647],{"className":5646},[147,148,149,150],[24,5648,4607],{"className":5649},[113,157,150],[24,5651,195],{"className":5652},[194],[24,5654,5656],{"className":5655},[130],[24,5657,5659],{"className":5658,"style":799},[134],[24,5660],{},[24,5662],{"className":5663,"style":213},[212],[24,5665,64],{"className":5666},[217],[24,5668],{"className":5669,"style":213},[212],[24,5671,5673,5676],{"className":5672},[104],[24,5674],{"className":5675,"style":4739},[108],[24,5677,5679,5682],{"className":5678},[113],[24,5680,53],{"className":5681,"style":190},[113,157],[24,5683,5685],{"className":5684},[414],[24,5686,5688,5708],{"className":5687},[125,126],[24,5689,5691,5705],{"className":5690},[130],[24,5692,5694],{"className":5693,"style":777},[134],[24,5695,5696,5699],{"style":4640},[24,5697],{"className":5698,"style":431},[142],[24,5700,5702],{"className":5701},[147,148,149,150],[24,5703,15],{"className":5704},[113,157,150],[24,5706,195],{"className":5707},[194],[24,5709,5711],{"className":5710},[130],[24,5712,5714],{"className":5713,"style":4778},[134],[24,5715],{},[10,5717,5719],{"id":5718},"利用皮卡逐步逼近序列求解ode的近似解","利用皮卡逐步逼近序列求解ODE的近似解",[15,5721,5722],{},[18,5723,20],{},[15,5725,5726],{},[24,5727,5729,5795],{"className":5728},[27],[24,5730,5732],{"className":5731},[31],[33,5733,5734],{"xmlns":35},[37,5735,5736,5792],{},[40,5737,5738,5752,5754,5757,5759,5761,5763,5765,5767,5769,5772,5774,5776,5782,5784,5786],{},[43,5739,5740,5746],{},[40,5741,5742,5744],{},[48,5743,50],{},[48,5745,53],{},[40,5747,5748,5750],{},[48,5749,50],{},[48,5751,60],{},[62,5753,81],{},[48,5755,5756],{},"f",[62,5758,71],{"stretchy":70},[48,5760,60],{},[62,5762,1827],{"separator":100},[48,5764,53],{},[62,5766,76],{"stretchy":70},[62,5768,1827],{"separator":100},[212,5770],{"width":5771},"1em",[48,5773,53],{},[62,5775,71],{"stretchy":70},[624,5777,5778,5780],{},[48,5779,60],{},[667,5781,739],{},[62,5783,76],{"stretchy":70},[62,5785,81],{},[624,5787,5788,5790],{},[48,5789,53],{},[667,5791,739],{},[92,5793,5794],{"encoding":94},"\\frac{dy}{dx} = f(x, y), \\quad y(x_0) = y_0",[24,5796,5798,5887,5983],{"className":5797,"ariaHidden":100},[99],[24,5799,5801,5804,5878,5881,5884],{"className":5800},[104],[24,5802],{"className":5803,"style":109},[108],[24,5805,5807,5810,5875],{"className":5806},[113],[24,5808],{"className":5809},[117,118],[24,5811,5813],{"className":5812},[43],[24,5814,5816,5867],{"className":5815},[125,126],[24,5817,5819,5864],{"className":5818},[130],[24,5820,5822,5839,5847],{"className":5821,"style":135},[134],[24,5823,5824,5827],{"style":138},[24,5825],{"className":5826,"style":143},[142],[24,5828,5830],{"className":5829},[147,148,149,150],[24,5831,5833,5836],{"className":5832},[113,150],[24,5834,50],{"className":5835},[113,157,150],[24,5837,60],{"className":5838},[113,157,150],[24,5840,5841,5844],{"style":163},[24,5842],{"className":5843,"style":143},[142],[24,5845],{"className":5846,"style":171},[170],[24,5848,5849,5852],{"style":174},[24,5850],{"className":5851,"style":143},[142],[24,5853,5855],{"className":5854},[147,148,149,150],[24,5856,5858,5861],{"className":5857},[113,150],[24,5859,50],{"className":5860},[113,157,150],[24,5862,53],{"className":5863,"style":190},[113,157,150],[24,5865,195],{"className":5866},[194],[24,5868,5870],{"className":5869},[130],[24,5871,5873],{"className":5872,"style":202},[134],[24,5874],{},[24,5876],{"className":5877},[208,118],[24,5879],{"className":5880,"style":247},[212],[24,5882,81],{"className":5883},[251],[24,5885],{"className":5886,"style":247},[212],[24,5888,5890,5893,5897,5900,5903,5906,5909,5912,5915,5918,5922,5925,5928,5931,5971,5974,5977,5980],{"className":5889},[104],[24,5891],{"className":5892,"style":227},[108],[24,5894,5756],{"className":5895,"style":5896},[113,157],"margin-right:0.1076em;",[24,5898,71],{"className":5899},[117],[24,5901,60],{"className":5902},[113,157],[24,5904,1827],{"className":5905},[1905],[24,5907],{"className":5908,"style":479},[212],[24,5910,53],{"className":5911,"style":190},[113,157],[24,5913,76],{"className":5914},[208],[24,5916,1827],{"className":5917},[1905],[24,5919],{"className":5920,"style":5921},[212],"margin-right:1em;",[24,5923],{"className":5924,"style":479},[212],[24,5926,53],{"className":5927,"style":190},[113,157],[24,5929,71],{"className":5930},[117],[24,5932,5934,5937],{"className":5933},[113],[24,5935,60],{"className":5936},[113,157],[24,5938,5940],{"className":5939},[414],[24,5941,5943,5963],{"className":5942},[125,126],[24,5944,5946,5960],{"className":5945},[130],[24,5947,5949],{"className":5948,"style":970},[134],[24,5950,5951,5954],{"style":780},[24,5952],{"className":5953,"style":431},[142],[24,5955,5957],{"className":5956},[147,148,149,150],[24,5958,739],{"className":5959},[113,150],[24,5961,195],{"className":5962},[194],[24,5964,5966],{"className":5965},[130],[24,5967,5969],{"className":5968,"style":799},[134],[24,5970],{},[24,5972,76],{"className":5973},[208],[24,5975],{"className":5976,"style":247},[212],[24,5978,81],{"className":5979},[251],[24,5981],{"className":5982,"style":247},[212],[24,5984,5986,5989],{"className":5985},[104],[24,5987],{"className":5988,"style":385},[108],[24,5990,5992,5995],{"className":5991},[113],[24,5993,53],{"className":5994,"style":190},[113,157],[24,5996,5998],{"className":5997},[414],[24,5999,6001,6021],{"className":6000},[125,126],[24,6002,6004,6018],{"className":6003},[130],[24,6005,6007],{"className":6006,"style":970},[134],[24,6008,6009,6012],{"style":4640},[24,6010],{"className":6011,"style":431},[142],[24,6013,6015],{"className":6014},[147,148,149,150],[24,6016,739],{"className":6017},[113,150],[24,6019,195],{"className":6020},[194],[24,6022,6024],{"className":6023},[130],[24,6025,6027],{"className":6026,"style":799},[134],[24,6028],{},[15,6030,6031],{},[18,6032,6033],{},"第零次近似：",[15,6035,6036],{},[24,6037,6039,6072],{"className":6038},[27],[24,6040,6042],{"className":6041},[31],[33,6043,6044],{"xmlns":35},[37,6045,6046,6069],{},[40,6047,6048,6055,6057,6059,6061,6063],{},[624,6049,6050,6053],{},[48,6051,6052],{},"ϕ",[667,6054,739],{},[62,6056,71],{"stretchy":70},[48,6058,60],{},[62,6060,76],{"stretchy":70},[62,6062,81],{},[624,6064,6065,6067],{},[48,6066,53],{},[667,6068,739],{},[92,6070,6071],{"encoding":94},"\\phi_0(x) = y_0",[24,6073,6075,6139],{"className":6074,"ariaHidden":100},[99],[24,6076,6078,6081,6121,6124,6127,6130,6133,6136],{"className":6077},[104],[24,6079],{"className":6080,"style":227},[108],[24,6082,6084,6087],{"className":6083},[113],[24,6085,6052],{"className":6086},[113,157],[24,6088,6090],{"className":6089},[414],[24,6091,6093,6113],{"className":6092},[125,126],[24,6094,6096,6110],{"className":6095},[130],[24,6097,6099],{"className":6098,"style":970},[134],[24,6100,6101,6104],{"style":780},[24,6102],{"className":6103,"style":431},[142],[24,6105,6107],{"className":6106},[147,148,149,150],[24,6108,739],{"className":6109},[113,150],[24,6111,195],{"className":6112},[194],[24,6114,6116],{"className":6115},[130],[24,6117,6119],{"className":6118,"style":799},[134],[24,6120],{},[24,6122,71],{"className":6123},[117],[24,6125,60],{"className":6126},[113,157],[24,6128,76],{"className":6129},[208],[24,6131],{"className":6132,"style":247},[212],[24,6134,81],{"className":6135},[251],[24,6137],{"className":6138,"style":247},[212],[24,6140,6142,6145],{"className":6141},[104],[24,6143],{"className":6144,"style":385},[108],[24,6146,6148,6151],{"className":6147},[113],[24,6149,53],{"className":6150,"style":190},[113,157],[24,6152,6154],{"className":6153},[414],[24,6155,6157,6177],{"className":6156},[125,126],[24,6158,6160,6174],{"className":6159},[130],[24,6161,6163],{"className":6162,"style":970},[134],[24,6164,6165,6168],{"style":4640},[24,6166],{"className":6167,"style":431},[142],[24,6169,6171],{"className":6170},[147,148,149,150],[24,6172,739],{"className":6173},[113,150],[24,6175,195],{"className":6176},[194],[24,6178,6180],{"className":6179},[130],[24,6181,6183],{"className":6182,"style":799},[134],[24,6184],{},[15,6186,6187],{},[18,6188,6189],{},"第一次近似：",[15,6191,6192],{},[24,6193,6195,6271],{"className":6194},[27],[24,6196,6198],{"className":6197},[31],[33,6199,6200],{"xmlns":35},[37,6201,6202,6268],{},[40,6203,6204,6210,6212,6214,6216,6218,6224,6226,6239,6241,6243,6246,6248,6254,6256,6258,6260,6262,6264,6266],{},[624,6205,6206,6208],{},[48,6207,6052],{},[667,6209,669],{},[62,6211,71],{"stretchy":70},[48,6213,60],{},[62,6215,76],{"stretchy":70},[62,6217,81],{},[624,6219,6220,6222],{},[48,6221,53],{},[667,6223,739],{},[62,6225,64],{},[6227,6228,6229,6231,6237],"msubsup",{},[62,6230,307],{},[624,6232,6233,6235],{},[48,6234,60],{},[667,6236,739],{},[48,6238,60],{},[48,6240,5756],{},[62,6242,71],{"stretchy":70},[48,6244,6245],{},"t",[62,6247,1827],{"separator":100},[624,6249,6250,6252],{},[48,6251,6052],{},[667,6253,739],{},[62,6255,71],{"stretchy":70},[48,6257,6245],{},[62,6259,76],{"stretchy":70},[62,6261,76],{"stretchy":70},[317,6263,319],{},[48,6265,50],{},[48,6267,6245],{},[92,6269,6270],{"encoding":94},"\\phi_1(x) = y_0 + \\int_{x_0}^{x} f(t, \\phi_0(t)) \\, dt",[24,6272,6274,6338,6393],{"className":6273,"ariaHidden":100},[99],[24,6275,6277,6280,6320,6323,6326,6329,6332,6335],{"className":6276},[104],[24,6278],{"className":6279,"style":227},[108],[24,6281,6283,6286],{"className":6282},[113],[24,6284,6052],{"className":6285},[113,157],[24,6287,6289],{"className":6288},[414],[24,6290,6292,6312],{"className":6291},[125,126],[24,6293,6295,6309],{"className":6294},[130],[24,6296,6298],{"className":6297,"style":970},[134],[24,6299,6300,6303],{"style":780},[24,6301],{"className":6302,"style":431},[142],[24,6304,6306],{"className":6305},[147,148,149,150],[24,6307,669],{"className":6308},[113,150],[24,6310,195],{"className":6311},[194],[24,6313,6315],{"className":6314},[130],[24,6316,6318],{"className":6317,"style":799},[134],[24,6319],{},[24,6321,71],{"className":6322},[117],[24,6324,60],{"className":6325},[113,157],[24,6327,76],{"className":6328},[208],[24,6330],{"className":6331,"style":247},[212],[24,6333,81],{"className":6334},[251],[24,6336],{"className":6337,"style":247},[212],[24,6339,6341,6344,6384,6387,6390],{"className":6340},[104],[24,6342],{"className":6343,"style":5620},[108],[24,6345,6347,6350],{"className":6346},[113],[24,6348,53],{"className":6349,"style":190},[113,157],[24,6351,6353],{"className":6352},[414],[24,6354,6356,6376],{"className":6355},[125,126],[24,6357,6359,6373],{"className":6358},[130],[24,6360,6362],{"className":6361,"style":970},[134],[24,6363,6364,6367],{"style":4640},[24,6365],{"className":6366,"style":431},[142],[24,6368,6370],{"className":6369},[147,148,149,150],[24,6371,739],{"className":6372},[113,150],[24,6374,195],{"className":6375},[194],[24,6377,6379],{"className":6378},[130],[24,6380,6382],{"className":6381,"style":799},[134],[24,6383],{},[24,6385],{"className":6386,"style":213},[212],[24,6388,64],{"className":6389},[217],[24,6391],{"className":6392,"style":213},[212],[24,6394,6396,6400,6499,6502,6505,6508,6511,6514,6517,6557,6560,6563,6566,6569,6572],{"className":6395},[104],[24,6397],{"className":6398,"style":6399},[108],"height:1.3152em;vertical-align:-0.4559em;",[24,6401,6403,6406],{"className":6402},[448],[24,6404,307],{"className":6405,"style":451},[448,449,450],[24,6407,6409],{"className":6408},[414],[24,6410,6412,6490],{"className":6411},[125,126],[24,6413,6415,6487],{"className":6414},[130],[24,6416,6419,6472],{"className":6417,"style":6418},[134],"height:0.8593em;",[24,6420,6422,6425],{"style":6421},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[24,6423],{"className":6424,"style":431},[142],[24,6426,6428],{"className":6427},[147,148,149,150],[24,6429,6431],{"className":6430},[113,150],[24,6432,6434,6437],{"className":6433},[113,150],[24,6435,60],{"className":6436},[113,157,150],[24,6438,6440],{"className":6439},[414],[24,6441,6443,6464],{"className":6442},[125,126],[24,6444,6446,6461],{"className":6445},[130],[24,6447,6450],{"className":6448,"style":6449},[134],"height:0.3173em;",[24,6451,6452,6455],{"style":2181},[24,6453],{"className":6454,"style":860},[142],[24,6456,6458],{"className":6457},[147,864,865,150],[24,6459,739],{"className":6460},[113,150],[24,6462,195],{"className":6463},[194],[24,6465,6467],{"className":6466},[130],[24,6468,6470],{"className":6469,"style":2200},[134],[24,6471],{},[24,6473,6475,6478],{"style":6474},"top:-3.2579em;margin-right:0.05em;",[24,6476],{"className":6477,"style":431},[142],[24,6479,6481],{"className":6480},[147,148,149,150],[24,6482,6484],{"className":6483},[113,150],[24,6485,60],{"className":6486},[113,157,150],[24,6488,195],{"className":6489},[194],[24,6491,6493],{"className":6492},[130],[24,6494,6497],{"className":6495,"style":6496},[134],"height:0.4559em;",[24,6498],{},[24,6500],{"className":6501,"style":479},[212],[24,6503,5756],{"className":6504,"style":5896},[113,157],[24,6506,71],{"className":6507},[117],[24,6509,6245],{"className":6510},[113,157],[24,6512,1827],{"className":6513},[1905],[24,6515],{"className":6516,"style":479},[212],[24,6518,6520,6523],{"className":6519},[113],[24,6521,6052],{"className":6522},[113,157],[24,6524,6526],{"className":6525},[414],[24,6527,6529,6549],{"className":6528},[125,126],[24,6530,6532,6546],{"className":6531},[130],[24,6533,6535],{"className":6534,"style":970},[134],[24,6536,6537,6540],{"style":780},[24,6538],{"className":6539,"style":431},[142],[24,6541,6543],{"className":6542},[147,148,149,150],[24,6544,739],{"className":6545},[113,150],[24,6547,195],{"className":6548},[194],[24,6550,6552],{"className":6551},[130],[24,6553,6555],{"className":6554,"style":799},[134],[24,6556],{},[24,6558,71],{"className":6559},[117],[24,6561,6245],{"className":6562},[113,157],[24,6564,2912],{"className":6565},[208],[24,6567],{"className":6568,"style":479},[212],[24,6570,50],{"className":6571},[113,157],[24,6573,6245],{"className":6574},[113,157],[15,6576,6577],{},[18,6578,6579,6580,6609],{},"第",[24,6581,6583,6596],{"className":6582},[27],[24,6584,6586],{"className":6585},[31],[33,6587,6588],{"xmlns":35},[37,6589,6590,6594],{},[40,6591,6592],{},[48,6593,631],{},[92,6595,631],{"encoding":94},[24,6597,6599],{"className":6598,"ariaHidden":100},[99],[24,6600,6602,6606],{"className":6601},[104],[24,6603],{"className":6604,"style":6605},[108],"height:0.4306em;",[24,6607,631],{"className":6608},[113,157],"次近似：",[15,6611,6612],{},[24,6613,6615,6695],{"className":6614},[27],[24,6616,6618],{"className":6617},[31],[33,6619,6620],{"xmlns":35},[37,6621,6622,6692],{},[40,6623,6624,6630,6632,6634,6636,6638,6644,6646,6658,6660,6662,6664,6666,6678,6680,6682,6684,6686,6688,6690],{},[624,6625,6626,6628],{},[48,6627,6052],{},[48,6629,631],{},[62,6631,71],{"stretchy":70},[48,6633,60],{},[62,6635,76],{"stretchy":70},[62,6637,81],{},[624,6639,6640,6642],{},[48,6641,53],{},[667,6643,739],{},[62,6645,64],{},[6227,6647,6648,6650,6656],{},[62,6649,307],{},[624,6651,6652,6654],{},[48,6653,60],{},[667,6655,739],{},[48,6657,60],{},[48,6659,5756],{},[62,6661,71],{"stretchy":70},[48,6663,6245],{},[62,6665,1827],{"separator":100},[624,6667,6668,6670],{},[48,6669,6052],{},[40,6671,6672,6674,6676],{},[48,6673,631],{},[62,6675,304],{},[667,6677,669],{},[62,6679,71],{"stretchy":70},[48,6681,6245],{},[62,6683,76],{"stretchy":70},[62,6685,76],{"stretchy":70},[317,6687,319],{},[48,6689,50],{},[48,6691,6245],{},[92,6693,6694],{"encoding":94},"\\phi_n(x) = y_0 + \\int_{x_0}^{x} f(t, \\phi_{n-1}(t)) \\, 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