| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+y^{\prime \prime \prime } = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = {\mathrm e}^{-2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y+y^{\prime \prime } = 4 x^{3}-8 x^{2}-14 x +7
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = {\mathrm e}^{x} \left (1+x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = x \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y-3 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x} \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}-1\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y+y^{\prime \prime } = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 x \,{\mathrm e}^{-x}+x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = 4 \cosh \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 3
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-7 y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = {\mathrm e}^{2 x} \left (x +3\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = x +2 \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+y^{\prime \prime \prime } = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y-3 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \frac {1}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-3 y = x \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y^{\prime \prime }+7 y^{\prime }+3 y = 5 \cos \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e i u^{\prime \prime \prime \prime } = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e i u^{\prime \prime \prime \prime } = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e i u^{\prime \prime \prime \prime } = \sinh \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e i u^{\prime \prime \prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e i u^{\prime \prime \prime \prime } = x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e i u^{\prime \prime \prime \prime } = x^{4}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{a x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sin \left (a x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{x}}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+10 y^{\prime }+25 y = \frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \csc \left (x \right ) \cot \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-12 y^{\prime }+36 y = {\mathrm e}^{6 x} \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-2 x} \sec \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{2 x}}{x^{4}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{-x} \ln \left (x \right )}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 5 x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = \sqrt {x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = x^{{1}/{4}} \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime } = \frac {1}{x^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y = \frac {\ln \left (x \right )}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{x}}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{2 x}}{x^{4}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime } = \frac {1}{x^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = \left (x^{2}+1\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x} = 0
\]
|
✓ |
✗ |
✓ |
|
| \[
{} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y = {\mathrm e}^{2 x} \left (1-2 x \ln \left (x \right )\right )^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+2 x^{\prime }+x = -\frac {{\mathrm e}^{-t}}{\left (t +1\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+6 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left [x_{1}^{\prime }\left (t \right ) = 2 \sin \left (t \right ) x_{1} \left (t \right )+\ln \left (t \right ) x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{t -2}+\frac {{\mathrm e}^{t} x_{2} \left (t \right )}{t +1}\right ]
\]
|
✗ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+\left (1-t \right ) x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{t}-x_{2} \left (t \right )\right ]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )+x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{3} \left (t \right )-x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{4} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-4 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = -10 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+4 x_{2} \left (t \right )+5 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -17 x_{1} \left (t \right )+x_{2} \left (t \right )+12 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )+3 \,{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [t x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), t y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-t^{2}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+2 t^{2}, y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )-1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [N_{1}^{\prime }\left (t \right ) = 4 N_{1} \left (t \right )-6 N_{2} \left (t \right ), N_{2}^{\prime }\left (t \right ) = 8 N_{1} \left (t \right )-10 N_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )+3 \,{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [t x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), t y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-t^{2}]
\]
|
✓ |
✓ |
✓ |
|