|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime \prime }+y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime \prime \prime }-y = x^{4}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} e y^{\prime \prime } = -P \left (L -x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} e y^{\prime \prime } = P \left (-y+a \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime } = 2 x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \csc \left (x \right )^{2} = \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (6 x +1\right ) y^{\prime }+6 y = \sin \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime } = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = -y a^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = \frac {1}{y^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+3 y^{\prime } = 3 x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x = y^{\prime \prime }+y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x = {y^{\prime }}^{2}+y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y = x y^{\prime }-{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} V^{\prime \prime }+\frac {V^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+7 y \left (x \right )-3 z \left (x \right ) = 0, 7 y^{\prime }\left (x \right )+63 y \left (x \right )-36 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+2 y^{\prime }\left (x \right )+3 y \left (x \right ) = 0, y^{\prime }\left (x \right )+3 y \left (x \right )-2 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )+3 y \left (x \right )+z \left (x \right ) = 0, z^{\prime }\left (x \right )+3 y \left (x \right )+5 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )+3 y \left (x \right )+2 z \left (x \right ) = 0, z^{\prime }\left (x \right )+2 y \left (x \right )-4 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )-3 y \left (x \right )-2 z \left (x \right ) = 0, z^{\prime }\left (x \right )+y \left (x \right )-2 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )+z^{\prime }\left (x \right )+6 y \left (x \right ) = 0, z^{\prime }\left (x \right )+5 y \left (x \right )+z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+y^{\prime }\left (x \right )+5 y \left (x \right )-3 z \left (x \right ) = x +{\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+y \left (x \right )+3 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )+3 y \left (x \right )+4 z \left (x \right ) = {\mathrm e}^{2 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )-3 y \left (x \right )+2 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{3 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = x, y^{\prime }\left (x \right )+4 y \left (x \right )+z \left (x \right ) = x]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+7 y \left (x \right )-9 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )-y \left (x \right )-3 z \left (x \right ) = {\mathrm e}^{2 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )-2 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{3 x}, z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{4 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} {y^{\prime }}^{2}+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-k^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (1-x \right ) y^{\prime }-1-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y-x y^{\prime } = a \left (y^{\prime }+y^{2}\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2}+y^{2}-2 x y y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (3 x +4 y\right ) y^{\prime }+y-2 x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y-x y^{\prime }+\ln \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x y+1\right ) y-x \left (1-x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} a \left (x y^{\prime }+2 y\right ) = x y y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y \left ({\mathrm e}^{x}+2 x y\right )-{\mathrm e}^{x} y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 y y^{\prime }+2 x +x^{2}+y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2}+y^{2}-x^{2} y y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 x^{2} y^{4}+2 x y+\left (2 y^{3} x^{3}-x^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-a y = 1+x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+y = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1+x \right ) y^{\prime }-n y = {\mathrm e}^{x} \left (1+x \right )^{n +1}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\frac {y}{x} = y^{6} x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x +y\right )^{2} y^{\prime } = a^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\]
|
✓ |
✓ |
✓ |
|