| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+2 t^{2}, y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )-1]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} \left [c_{1}^{\prime }\left (t \right ) = -\frac {k c_{1} \left (t \right )}{V_{1}}+\frac {k c_{2} \left (t \right )}{V_{1}}, c_{2}^{\prime }\left (t \right ) = \frac {k c_{1} \left (t \right )}{V_{2}}-\frac {k c_{2} \left (t \right )}{V_{2}}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = a \left (b -x \left (t \right )\right )-c f y \left (t \right ), y^{\prime }\left (t \right ) = d \left (x \left (t \right )-y \left (t \right )\right )-c f y \left (t \right )-a y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 17 x \left (t \right )-7 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 12 x \left (t \right )-7 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-4 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )-4 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-8 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )-8 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right )-w \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+2 z \left (t \right )+2 w \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+2 w \left (t \right ), w^{\prime }\left (t \right ) = -3 y \left (t \right )-6 z \left (t \right )-6 w \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), z^{\prime }\left (t \right ) = 2 z \left (t \right )+w \left (t \right )+h \left (t \right ), w^{\prime }\left (t \right ) = z \left (t \right )+2 w \left (t \right )+h \left (t \right ), h^{\prime }\left (t \right ) = z \left (t \right )+w \left (t \right )+2 h \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -10 x \left (t \right )+y \left (t \right )+7 z \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+4 y \left (t \right )+5 z \left (t \right ), z^{\prime }\left (t \right ) = -17 x \left (t \right )+y \left (t \right )+12 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-4 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )-4 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-8 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )-8 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -10 x \left (t \right )+y \left (t \right )+7 z \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+4 y \left (t \right )+5 z \left (t \right ), z^{\prime }\left (t \right ) = -17 x \left (t \right )+y \left (t \right )+12 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 z \left (t \right ), u^{\prime }\left (t \right ) = 5 z \left (t \right )]
\]
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| \[
{} y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }+4 y = 4 \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }-4 y = 0
\]
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| \[
{} y^{\prime }-3 y = 13 \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-y = 6 \,{\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }-4 y = -3 \,{\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }+10 y^{\prime }+25 y = 2 \,{\mathrm e}^{-5 t}
\]
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| \[
{} y^{\prime \prime \prime }-27 y = 0
\]
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| \[
{} y^{\prime \prime }-9 y^{\prime }+18 y = 54
\]
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| \[
{} y^{\prime \prime }-9 y = 20 \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+9 y = {\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 24 \cosh \left (t \right )
\]
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| \[
{} y^{\prime \prime }+10 y^{\prime }+26 y = 37 \,{\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime \prime }-y = -1
\]
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| \[
{} y^{\prime \prime \prime }+y = -1
\]
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| \[
{} y^{\prime }-3 y = 2 \,{\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 27 t
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-6 y = \cos \left (t \right )+57 \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }-4 y = 25 t \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+13 y^{\prime }+36 y = 10-72 t
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 16 t \,{\mathrm e}^{-t}-15
\]
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| \[
{} y^{\prime \prime }-10 y^{\prime }+21 y = 21 t^{2}+t +13
\]
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| \[
{} y^{\prime \prime }+7 y^{\prime }+10 y = 3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t}
\]
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| \[
{} 4 y^{\prime \prime }-3 y^{\prime }-y = 34 \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime \prime }-y = 12 \sinh \left (t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 3 t^{3}-9 t^{2}-5 t +1
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 39 \,{\mathrm e}^{t} \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t}+5 t
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 3 t \,{\mathrm e}^{2 t}-4
\]
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| \[
{} y^{\prime \prime \prime }+y = 18 \,{\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime \prime }+8 y = -12 \,{\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }-y = 2 t^{2}+2 \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+7 y^{\prime }+6 y = 250 \,{\mathrm e}^{t} \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 13 t +17+40 \sin \left (t \right )
\]
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| \[
{} y^{\prime } = 3 y
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = 0
\]
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| \[
{} \left (1-x \right ) y^{\prime \prime }-y^{\prime }+x y = 0
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\]
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| \[
{} \left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-\left (x +2\right ) y = 0
\]
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| \[
{} x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+x y = 0
\]
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| \[
{} \left (x -1\right )^{4} y^{\prime \prime }-x y = 0
\]
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| \[
{} y^{\prime \prime }-x y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+p^{2} y = 0
\]
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| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }-2 x y^{\prime }+p y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+p y = 0
\]
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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y = 0
\]
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| \[
{} \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+x y = 0
\]
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