| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-3 y = 4 t^{2} \cos \left (t \right )
\]
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{} y^{\prime \prime }+4 y = 32 t \cos \left (2 t \right )
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{} y^{\prime \prime }-y y^{\prime } = 6
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{} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{t}
\]
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{} y^{\prime \prime \prime }+y^{\prime }+4 y = 0
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{} y^{\prime \prime }+\sin \left (y\right ) = 0
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| \[
{} t y^{\prime }+y = \ln \left (t \right )
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{} y^{\prime \prime }+2 y^{\prime }+3 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }-7 y^{\prime }+10 y = 0
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{} y^{\prime \prime }+8 y = t
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{} y^{\prime \prime }+2 = \cos \left (t \right )
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{} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0
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{} y^{\prime \prime }-y^{\prime }-2 y = 0
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{} y^{\prime \prime }+y^{\prime }-12 y = 0
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{} y^{\prime \prime }+10 y^{\prime }+24 y = 0
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{} y^{\prime \prime }-4 y^{\prime }-12 y = 0
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{} y^{\prime \prime }+8 y^{\prime }+16 y = 0
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| \[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 0
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
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| \[
{} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0
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{} y^{\prime \prime }+13 y^{\prime }+36 y = 0
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{} y^{\prime \prime }+8 y^{\prime }+25 y = 0
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| \[
{} y^{\prime \prime }+10 y^{\prime }+25 y = 0
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{} y^{\prime \prime }-4 y^{\prime }-21 y = 0
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{} y^{\prime \prime }-y = 0
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{} y^{\prime \prime }-3 y^{\prime }-10 y = 0
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{} y^{\prime \prime }-10 y^{\prime }+25 y = 0
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{} y^{\prime \prime }+4 y^{\prime }+13 y = 0
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{} y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{2 t}
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| \[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{2 t}
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{t}
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
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{} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-3 t}
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| \[
{} y^{\prime \prime }+4 y = 1+{\mathrm e}^{t}
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{} y^{\prime \prime }-y = t^{2}
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{t}
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t}
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| \[
{} y^{\prime \prime }+y = 2 \sin \left (t \right )
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| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t}
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{-3 t}
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{} y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 t} \cos \left (2 t \right )
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{} y^{\prime \prime }-8 y^{\prime }+25 y = 104 \sin \left (3 t \right )
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{} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 t}
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{-t}
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{} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 t}
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| \[
{} y^{\prime \prime }-4 y = 2-8 t
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{} y^{\prime \prime }-4 y = {\mathrm e}^{-6 t}
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| \[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 16 \,{\mathrm e}^{t}
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{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 t}
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
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{} y^{\prime \prime }+2 y^{\prime }-8 y = 6 \,{\mathrm e}^{-4 t}
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{} y^{\prime \prime }+3 y^{\prime }-10 y = \sin \left (t \right )
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t}
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{} y^{\prime \prime }-5 y^{\prime }-6 y = 10 t \,{\mathrm e}^{4 t}
\]
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{} y^{\prime \prime }-8 y^{\prime }+25 y = 36 t \,{\mathrm e}^{4 t} \sin \left (3 t \right )
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \cos \left (t \right )
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| \[
{} y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{t} \cos \left (t \right )
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| \[
{} y^{\prime \prime \prime }-3 y^{\prime } = {\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime \prime \prime }+y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime \prime \prime }+y^{4} = 0
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| \[
{} y^{\left (5\right )}+t y^{\prime \prime }-3 y = 0
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| \[
{} y^{\prime \prime \prime }-y = 0
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{} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
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{} y^{\prime \prime \prime \prime }-y = 0
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| \[
{} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = 0
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{} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
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{} y^{\prime \prime \prime }-2 y^{\prime \prime }-25 y^{\prime }+50 y = 0
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{} y^{\prime \prime \prime }+2 y^{\prime \prime }+25 y^{\prime }+50 y = 0
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{} y^{\left (6\right )}+27 y^{\prime \prime \prime \prime }+243 y^{\prime \prime }+729 y = 0
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{} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+18 y^{\prime \prime }-27 y = 0
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| \[
{} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
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{} y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{t}
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{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 4 \cos \left (t \right )
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{} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{2 t}
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{} y^{\prime \prime \prime \prime }-y = {\mathrm e}^{t}+{\mathrm e}^{-t}
\]
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{} y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{t}
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{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime } = 4 t \,{\mathrm e}^{2 t}
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| \[
{} y^{\prime \prime \prime }+4 y^{\prime } = t
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{} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{2 t}
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{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 4 \cos \left (t \right )
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{} y^{\prime \prime \prime \prime }-y = {\mathrm e}^{t}+{\mathrm e}^{-t}
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-6 y_{1} \left (t \right ) = -4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-3 y_{1} \left (t \right ) = -4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = 2 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = -2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )+4 y_{1} \left (t \right ) = 10 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-6 y_{2}^{\prime }\left (t \right )+23 y_{2} \left (t \right ) = 9 y_{1} \left (t \right )]
\]
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{} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = -2 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+y_{2}^{\prime }\left (t \right )+6 y_{2} \left (t \right ) = 4 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1}^{\prime }\left (t \right )+6 y_{1} \left (t \right ) = 5 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-2 y_{2}^{\prime }\left (t \right )+6 y_{2} \left (t \right ) = 9 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1} \left (t \right ) = -3 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )-9 y_{2} \left (t \right ) = 6 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )-2 y_{2} \left (t \right ) = y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-y_{1} \left (t \right ) = -2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )-y_{2} \left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )+2 y_{1} \left (t \right ) = 5 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-2 y_{2}^{\prime }\left (t \right )+5 y_{2} \left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1} \left (t \right ) = -3 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )-9 y_{2} \left (t \right ) = 6 y_{1} \left (t \right )]
\]
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| \[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = t^{2}
\]
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| \[
{} y^{\prime \prime }+t y^{\prime }+\left (t^{2}+1\right )^{2} y^{2} = 0
\]
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| \[
{} 3 t^{2} y^{\prime \prime }+2 t y^{\prime }+y = {\mathrm e}^{2 t}
\]
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