5.7.2 Problems 101 to 200

Table 5.565: Solved using series method

#

ODE

Mathematica

Maple

501

\[ {}5 x y^{\prime \prime }+\left (30+3 x \right ) y^{\prime }+3 y = 0 \]

502

\[ {}x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y = 0 \]

503

\[ {}2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y = 0 \]

504

\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \]

505

\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

506

\[ {}x y^{\prime \prime }+y^{\prime }-x y = 0 \]

507

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

508

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y = 0 \]

509

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \]

510

\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y = 0 \]

511

\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-4 y = 0 \]

512

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \]

513

\[ {}x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \]

1042

\[ {}y^{\prime } = y \]

1043

\[ {}y^{\prime } = 4 y \]

1044

\[ {}2 y^{\prime }+3 y = 0 \]

1045

\[ {}y^{\prime }+2 x y = 0 \]

1046

\[ {}y^{\prime } = x^{2} y \]

1047

\[ {}\left (x -2\right ) y^{\prime }+y = 0 \]

1048

\[ {}\left (2 x -1\right ) y^{\prime }+2 y = 0 \]

1049

\[ {}2 \left (1+x \right ) y^{\prime } = y \]

1050

\[ {}\left (x -1\right ) y^{\prime }+2 y = 0 \]

1051

\[ {}2 \left (x -1\right ) y^{\prime } = 3 y \]

1052

\[ {}y^{\prime \prime } = y \]

1053

\[ {}y^{\prime \prime } = 4 y \]

1054

\[ {}y^{\prime \prime }+9 y = 0 \]

1055

\[ {}y^{\prime \prime }+y = x \]

1056

\[ {}x y^{\prime }+y = 0 \]

1057

\[ {}2 x y^{\prime } = y \]

1058

\[ {}x^{2} y^{\prime }+y = 0 \]

1059

\[ {}x^{3} y^{\prime } = 2 y \]

1060

\[ {}y^{\prime \prime }+4 y = 0 \]

1061

\[ {}y^{\prime \prime }-4 y = 0 \]

1062

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

1063

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]

1064

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \]

1066

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

1067

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

1068

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

1069

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

1070

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

1071

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

1072

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

1073

\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0 \]

1074

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

1075

\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

1076

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

1077

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

1078

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \]

1079

\[ {}y^{\prime \prime }+x y = 0 \]

1080

\[ {}y^{\prime \prime }+x^{2} y = 0 \]

1081

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

1082

\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

1083

\[ {}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0 \]

1084

\[ {}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0 \]

1085

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]

1086

\[ {}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y \]

1087

\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]

1088

\[ {}y^{\prime \prime }+\left (1+x \right ) y = 0 \]

1089

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0 \]

1090

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \]

1091

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0 \]

1092

\[ {}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \]

1093

\[ {}y^{\prime \prime }+{\mathrm e}^{-x} y = 0 \]

1094

\[ {}y^{\prime \prime } \cos \left (x \right )+y = 0 \]

1095

\[ {}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+x y = 0 \]

1096

\[ {}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \]

1097

\[ {}y^{\prime \prime } = x y \]

1361

\[ {}y^{\prime \prime }-y = 0 \]

1362

\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \]

1363

\[ {}y^{\prime \prime }+k^{2} x^{2} y = 0 \]

1364

\[ {}\left (1-x \right ) y^{\prime \prime }+y = 0 \]

1365

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]

1366

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

1367

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

1368

\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0 \]

1369

\[ {}\left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \]

1370

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

1371

\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

1372

\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \]

1373

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]

1374

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

1375

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

1376

\[ {}y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \]

1377

\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \]

1378

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]

1379

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

1380

\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

1381

\[ {}y^{\prime \prime }+x^{2} y = 0 \]

1382

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

1383

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

1384

\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0 \]

1385

\[ {}x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y \ln \left (x \right ) = 0 \]

1386

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+y \sin \left (x \right ) = 0 \]

1387

\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \]

1388

\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \]

1389

\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

1390

\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

1391

\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

1392

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \]