4.24.52 Problems 5101 to 5200

Table 4.1455: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

22194

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

22197

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

22198

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

22201

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

22202

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

22204

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

22205

\[ {} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y = 5 \sin \left (x \right ) \]

22271

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

22272

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

22408

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

22412

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

22418

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

22431

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

22433

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

22441

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

22446

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

22472

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

22473

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

22575

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

22598

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

22599

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

22600

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

22602

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

22604

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

22605

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

22606

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

22607

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

22610

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

22611

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

22613

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

22614

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

22615

\[ {} y^{\prime \prime } = -\frac {4}{y^{3}} \]

22616

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

22681

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

22690

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

22694

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

22695

\[ {} x^{4} y^{\prime \prime \prime }+1 = 0 \]

22706

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{r} = 4-4 r \]

22732

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

22736

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

22738

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

22743

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

22754

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

22767

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

22768

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

22769

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

22798

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

22799

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

22801

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

22854

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

22868

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

22869

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

22870

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

22871

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

22872

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{2}+16 \ln \left (x \right )^{2} \]

22873

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

22874

\[ {} t^{2} i^{\prime \prime }+2 i^{\prime } t +i = t \ln \left (t \right ) \]

22875

\[ {} y^{\prime \prime } = \frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}} \]

22876

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = \sqrt {x}+\frac {1}{\sqrt {x}} \]

22877

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime } = 5 \ln \left (x \right ) \]

22878

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

22879

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

22880

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y = 1 \]

22881

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

22882

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

22883

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

22884

\[ {} \left (2 x +3\right )^{2} y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }-2 y = 24 x^{2} \]

22885

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

22886

\[ {} \left (r^{2}+r \right ) R^{\prime \prime }+r R^{\prime }-n \left (n +1\right ) R = 0 \]

22887

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

22888

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

22889

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

22890

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

22891

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

22899

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

22906

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 24+24 x \]

22911

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

22913

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

22914

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

22915

\[ {} y^{\prime \prime \prime } = \frac {24 x +24 y}{x^{3}} \]

22916

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

22917

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

22918

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

22921

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

22933

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

23161

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

23162

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

23163

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

23164

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

23165

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

23197

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

23217

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

23220

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

23221

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

23222

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

23225

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

23233

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

23344

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

23346

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

23347

\[ {} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{x} = 0 \]