4.24.46 Problems 4501 to 4600

Table 4.1443: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

19284

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

19285

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

19286

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

19287

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

19288

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

19289

\[ {} -2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime } = x^{4}+12 \]

19292

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

19294

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

19295

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

19312

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

19313

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

19314

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

19315

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

19316

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

19317

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

19318

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

19319

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

19320

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

19321

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

19322

\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \]

19323

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

19329

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

19330

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

19473

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

19474

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

19476

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

19477

\[ {} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \]

19478

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

19479

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

19480

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

19481

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

19482

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

19483

\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]

19484

\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]

19485

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

19491

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

19495

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

19500

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

19507

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

19508

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

19519

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

19525

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

19530

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

19533

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

19535

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

19536

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

19538

\[ {} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 1 \]

19544

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

19546

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

19547

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

19549

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

19552

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

19556

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

19557

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

19560

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

19561

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

19562

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

19563

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

19564

\[ {} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0 \]

19565

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

19566

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

19567

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

19568

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

19569

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

19570

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

19571

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

19572

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

19573

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

19598

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

19599

\[ {} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

19600

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

19601

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

19602

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

19603

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

19604

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

19605

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

19606

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

19607

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

19608

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

19638

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

19639

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

19640

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

19641

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

19642

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]

19662

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

19663

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

19664

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

19665

\[ {} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \]

19700

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

19744

\[ {} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y = 0 \]

19745

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

19746

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

19773

\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

19799

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

19802

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

19817

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

19819

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

19820

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

19822

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

19824

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