3.24.31 Problems 3001 to 3100

Table 3.867: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

13252

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

13271

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

13473

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

13474

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

13477

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

13478

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

13479

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

13480

\[ {}y^{\prime } y^{\prime \prime } = 1 \]

13481

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

13482

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

13483

\[ {}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \]

13484

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

13486

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

13489

\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \]

13490

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

13492

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

13493

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

13494

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

13496

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

13497

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

13498

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

13499

\[ {}y^{\prime } y^{\prime \prime } = 1 \]

13500

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

13501

\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \]

13502

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

13503

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

13504

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

13506

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

13507

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

13508

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

13512

\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \]

13513

\[ {}x y^{\prime \prime }+2 y^{\prime } = 6 \]

13514

\[ {}2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1 \]

13515

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

13516

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

13517

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

13518

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

13519

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

13520

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

13521

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

13522

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

13523

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

13524

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

13525

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

13526

\[ {}y^{\prime \prime }+x^{2} y^{\prime }-4 y = x^{3} \]

13527

\[ {}y^{\prime \prime }+x^{2} y^{\prime }-4 y = 0 \]

13528

\[ {}y^{\prime \prime }+x^{2} y^{\prime } = 4 y \]

13529

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3} \]

13532

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

13535

\[ {}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y \]

13538

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

13539

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

13540

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]

13541

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

13542

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

13543

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y = 0 \]

13545

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

13546

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

13547

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

13548

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

13549

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

13552

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

13553

\[ {}x^{2} y^{\prime \prime }-20 y = 27 x^{5} \]

13554

\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

13555

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

13559

\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \]

13564

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

13565

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \]

13566

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

13567

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

13568

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

13569

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

13570

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

13643

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \]

13644

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

13645

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

13646

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

13647

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

13648

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

13649

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]

13650

\[ {}x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0 \]

13651

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0 \]

13652

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

13653

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0 \]

13654

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

13655

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

13656

\[ {}4 x^{2} y^{\prime \prime }+37 y = 0 \]

13657

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

13658

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-25 y = 0 \]

13659

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y = 0 \]

13660

\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0 \]

13661

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

13662

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \]

13663

\[ {}x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0 \]

13664

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

13665

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

13666

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

13667

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

13668

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

13669

\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = 0 \]