5.3.53 Problems 5201 to 5300

Table 5.139: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

17728

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

17730

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

17731

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

17732

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

17733

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

17734

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

17805

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

17818

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

17819

\[ {} [x^{\prime }\left (t \right ) = 1+5 y \left (t \right ), y^{\prime }\left (t \right ) = 1-6 x \left (t \right )^{2}] \]

17823

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

17833

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

17848

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

17849

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

17853

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

17854

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

17855

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

17856

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

17857

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

17860

\[ {} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0 \]

17861

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

17864

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

17866

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

17870

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

17875

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

17877

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

17878

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

17879

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

17881

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

17882

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

17883

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

17894

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

17896

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

17898

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

17900

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

17901

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

17903

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

17904

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

17905

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

17906

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

17907

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

17908

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

17909

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

17910

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

17911

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

17912

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

17913

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

17914

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

17915

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

17916

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

17917

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

17918

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

17919

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

17920

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

17921

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

17924

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

17926

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

17928

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

17929

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

17931

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

17932

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

17935

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

17937

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

17938

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

17960

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

17963

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

17965

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

17966

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

17969

\[ {} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )}{2}\right ] \]

17970

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

17972

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

17973

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

17975

\[ {} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}\right ] \]

17981

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

17991

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

18040

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

18048

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

18054

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

18055

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

18058

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

18061

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

18063

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

18067

\[ {} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0 \]

18071

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

18073

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

18074

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

18078

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

18081

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

18082

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

18092

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

18093

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

18097

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

18115

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

18116

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

18120

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

18121

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

18124

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

18125

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

18127

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

18128

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

18131

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