4.24.30 Problems 2901 to 3000

Table 4.1069: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

13465

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

13466

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

13467

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

13468

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

13469

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

13470

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

13471

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

13472

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

13473

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

13474

\[ {} x^{2} y^{\prime \prime }-2 y = 4 x -8 \]

13475

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \]

13476

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \]

13477

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

13478

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

13479

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

13480

\[ {} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

13583

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

13584

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

13585

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

13586

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

13587

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

13588

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

13589

\[ {} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0 \]

13590

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

13591

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

13592

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

13593

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

13594

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

13595

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

13596

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

13597

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

13598

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

13603

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

13604

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

13605

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

13606

\[ {} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0 \]

13619

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

13620

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

13621

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

13622

\[ {} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0 \]

13623

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

13705

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

13706

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

13707

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

13708

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

13709

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

13710

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

13714

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

13716

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

13717

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

13718

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

13719

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

13720

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

13721

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

13722

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

13723

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

13724

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

13725

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

13726

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

13825

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

13827

\[ {} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0 \]

13829

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

13830

\[ {} x^{3} x^{\prime \prime }+1 = 0 \]

13832

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

13836

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

13837

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

13838

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

13840

\[ {} u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

13841

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

13842

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

13847

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

13848

\[ {} m x^{\prime \prime } = f \left (x\right ) \]

13849

\[ {} m x^{\prime \prime } = f \left (x^{\prime }\right ) \]

13852

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

13853

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

13857

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

13860

\[ {} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

13861

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

13863

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

13864

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

13879

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

13880

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

13881

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

13883

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

13884

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

13886

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

13891

\[ {} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \]

13893

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

13895

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

13897

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

13898

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

13899

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

13900

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

13905

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

13906

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

13907

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

13908

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

13909

\[ {} y^{\prime \prime } \sin \left (x \right )+x y^{\prime }+7 y = 1 \]

13910

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

13911

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