4.24.36 Problems 3501 to 3600

Table 4.1081: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

17554

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

17555

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

17556

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

17557

\[ {} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0 \]

17558

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

17559

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

17593

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

17594

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x \]

17595

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

17596

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

17606

\[ {} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

17607

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

17620

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

17621

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

17622

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

17623

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

17624

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

17625

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

17626

\[ {} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

17627

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

17628

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

17629

\[ {} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \]

17631

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

17632

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

17716

\[ {} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right ) \]

17717

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

17718

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

17719

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

17720

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

17722

\[ {} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right ) \]

17723

\[ {} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0 \]

17724

\[ {} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right ) \]

17725

\[ {} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (5+x \right ) y^{\prime \prime }+\tan \left (x \right ) y = 0 \]

17726

\[ {} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0 \]

17733

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

17734

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

17892

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

17893

\[ {} a^{3} y^{\prime \prime \prime } y^{\prime \prime } = \sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \]

17894

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

17895

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

17896

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

17897

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

17898

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

17899

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

17900

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

17901

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

17902

\[ {} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0 \]

17903

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

17904

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

17905

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

17906

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

17907

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

17908

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

17909

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

17910

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

17911

\[ {} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0 \]

17912

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

17913

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

17914

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

17915

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

17916

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

17917

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

17918

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

17919

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

17920

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

17921

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

17922

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

17923

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

17924

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

17927

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

17929

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

17930

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

17947

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

17948

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

17949

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

17950

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

17951

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

17952

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

17953

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

17954

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

17955

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

17956

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

17957

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

17958

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

17964

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

17965

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

18108

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

18109

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

18111

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

18112

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

18113

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

18114

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

18115

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

18116

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

18117

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

18118

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

18119

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

18120

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

18126

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

18130

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