5.3.47 Problems 4601 to 4700

Table 5.127: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

13795

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

13796

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

13798

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

13799

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

13800

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

13803

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

13804

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

13810

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

13816

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

13823

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

13827

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

13835

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

13838

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

13840

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

13845

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

13846

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

13849

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

13850

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

13852

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

13855

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

13856

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

13857

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

13860

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

13861

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

13865

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

13868

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

13871

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

13872

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

13879

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

13883

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

13885

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

13887

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

13888

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

13889

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

13890

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

13891

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

13892

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

13893

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

13894

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

13896

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

13899

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

13903

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

13904

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

13905

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

13906

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

13908

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

13913

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

13914

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

13915

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

13916

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

13917

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

13918

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

13919

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

13920

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

13921

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

13922

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

13923

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

13924

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

13925

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

13926

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

13927

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

13928

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

13929

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

13930

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

13931

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

13932

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

13933

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

13934

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

13935

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

13936

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

13937

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

13938

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

13939

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

13940

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

13941

\[ {} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

13942

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

13943

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

13944

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

13945

\[ {} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0 \]

13946

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

13947

\[ {} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

13998

\[ {} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

13999

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]

14000

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]

14013

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

14017

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

14018

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

14019

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

14020

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

14053

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}] \]

14059

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

14063

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

14071

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

14072

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

14075

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

14081

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

14082

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

14085

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

14086

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

14089

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