| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime } = t +y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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| \[
{} y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\]
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| \[
{} y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\]
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| \[
{} y^{\prime } = t^{2}+y^{2}
\]
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| \[
{} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\]
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| \[
{} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\]
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| \[
{} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\]
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| \[
{} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\]
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| \[
{} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\]
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| \[
{} t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y = 0
\]
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| \[
{} t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\]
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| \[
{} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\]
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| \[
{} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y = 0
\]
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| \[
{} \frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1}
\]
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| \[
{} {\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\]
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| \[
{} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} 1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0
\]
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| \[
{} \sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0
\]
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| \[
{} 2 t \cos \left (y\right )+3 t^{2} y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\]
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| \[
{} 3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\]
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| \[
{} 2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = t^{2}+y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{t}+y^{2}
\]
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| \[
{} y^{\prime } = y^{2}+\cos \left (t \right )^{2}
\]
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| \[
{} y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\]
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| \[
{} y^{\prime } = t +y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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| \[
{} y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\]
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| \[
{} y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\]
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| \[
{} y^{\prime } = t^{2}+y^{2}
\]
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| \[
{} y^{\prime } = t y^{a}
\]
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| \[
{} y^{\prime } = y+{\mathrm e}^{-y}+2 t
\]
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| \[
{} y^{\prime } = 1-t +y^{2}
\]
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| \[
{} y^{\prime } = \frac {t^{2}+y^{2}}{1+t +y^{2}}
\]
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| \[
{} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\]
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| \[
{} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\]
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| \[
{} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\]
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| \[
{} t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y = 0
\]
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| \[
{} y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\]
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| \[
{} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\]
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| \[
{} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = {\mathrm e}^{t}
\]
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| \[
{} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\]
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| \[
{} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\]
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| \[
{} t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y = 0
\]
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| \[
{} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\]
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| \[
{} t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y = 0
\]
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| \[
{} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+7 y = \left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 y \left (t \right )^{2}-3 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -b x \left (t \right ) y \left (t \right )+m, y^{\prime }\left (t \right ) = b x \left (t \right ) y \left (t \right )-g y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )-b x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -c y \left (t \right )+d x \left (t \right ) y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )+x \left (t \right )^{2}+y \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-x \left (t \right ) y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -y \left (t \right )-y \left (t \right ) x \left (t \right )^{2}, z^{\prime }\left (t \right ) = 1-z \left (t \right )+x \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )^{2}-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) \sin \left (\pi y \left (t \right )\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ), y^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right )-1]
\]
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✓ |
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| \[
{} [x^{\prime }\left (t \right ) = -1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right ), z^{\prime }\left (t \right ) = x \left (t \right )+\sin \left (z \left (t \right )\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{z \left (t \right )}-x \left (t \right )]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {\left (x_{1} \left (t \right )^{2}+\sqrt {x_{1} \left (t \right )^{2}+4 x_{2} \left (t \right )^{2}}\right ) x_{1} \left (t \right )}{2}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}+1, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}-1, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \tan \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right )+x \left (t \right )^{3}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = {\mathrm e}^{y \left (t \right )}-x \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{x \left (t \right )}+y \left (t \right )]
\]
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✓ |
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| \[
{} z^{\prime \prime }+z+z^{5} = 0
\]
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✓ |
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| \[
{} z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\]
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| \[
{} z^{\prime \prime }+z-2 z^{3} = 0
\]
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✓ |
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| \[
{} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\]
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| \[
{} \left (x^{2}+3 x \right ) y^{\prime } = y^{3}+2 y
\]
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