| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+2 y = x +{\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime \prime }+2 y = {\mathrm e}^{x}+2
\]
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{} y^{\prime \prime }-y = 2 \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+y = \sin \left (x \right )
\]
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{} y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+3 y = x^{3}+\sin \left (x \right )
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}+2
\]
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| \[
{} y^{\prime \prime }+2 n y^{\prime }+n^{2} y = A \cos \left (p x \right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left (x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }-2 y = x^{2}+1
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8} = \frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}-2 \,{\mathrm e}^{2 x}+\sin \left (x \right )
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{} y^{\prime \prime }-4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (2 x \right ) x
\]
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{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
\]
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{} y^{\prime \prime }+9 y = 8 \sin \left (x \right )
\]
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{} 25 y^{\prime \prime }-30 y^{\prime }+9 y = 0
\]
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| \[
{} 9 y^{\prime \prime }-6 y^{\prime }+y = \left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x}
\]
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| \[
{} x y^{\prime \prime } = x +y^{\prime }
\]
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{} y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right )
\]
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{} y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right )
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{} y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right )
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 36 x \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }+3 y^{\prime }+5 y = 5 \sin \left (2 x \right ) {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2}
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x} \left (1+x \right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+5 y = 4 \cos \left (2 x \right ) {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+4 y = 4 \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-y = 12 x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right )
\]
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{} y^{\prime \prime }+y = 2 \sin \left (x \right )-3 \cos \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (x^{2}+10\right )
\]
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{} y^{\prime \prime }-4 y = 96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x}
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (x \right )+10 \sin \left (2 x \right )
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{} y^{\prime \prime }-2 y^{\prime }+2 y = 4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \sin \left (2 x \right ) x
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{} y^{\prime \prime }-y = \frac {1}{x}-\frac {2}{x^{3}}
\]
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{} y^{\prime \prime }-y = \frac {1}{\sinh \left (x \right )}
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{x}\right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
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{} y^{\prime \prime }-y = \frac {1}{\sqrt {1-{\mathrm e}^{2 x}}}
\]
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{} y^{\prime \prime }-y = {\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 15 \,{\mathrm e}^{-x} \sqrt {1+x}
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
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| \[
{} y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1}
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
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{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
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{} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
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{} y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right )
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{} y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1
\]
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{} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}
\]
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{} y^{\prime \prime }-2 y^{\prime }+2 y = 8 \sin \left (t \right ) {\mathrm e}^{-t}
\]
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{} y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right )
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{} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
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{} y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
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{} y^{\prime \prime }+4 y = 8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
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{} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
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{} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\]
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{} y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
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| \[
{} y^{\prime \prime } = 0
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{} y^{\prime \prime } = x +\sin \left (x \right )
\]
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| \[
{} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x}
\]
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| \[
{} y^{\prime \prime }+y = 0
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{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }+y = a x
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{} y^{\prime \prime }+y = a \cos \left (b x \right )
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{} y^{\prime \prime }+y = 8 \cos \left (x \right ) \cos \left (2 x \right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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{} y^{\prime \prime }+y = a \sin \left (b x \right )
\]
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{} y^{\prime \prime }+y = \sin \left (a x \right ) \sin \left (b x \right )
\]
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{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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{} y^{\prime \prime }+y = x \left (\cos \left (x \right )-x \sin \left (x \right )\right )
\]
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{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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{} y^{\prime \prime }+y = {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+y = {\mathrm e}^{x} \left (x^{2}-1\right )
\]
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{} y^{\prime \prime }+y = \sin \left (2 x \right ) {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{2 x} \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }-2 y = 0
\]
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| \[
{} y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\]
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{} y^{\prime \prime }+4 y = 0
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{} y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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| \[
{} -a^{2} y+y^{\prime \prime } = 1+x
\]
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{} y^{\prime \prime } = a x +b y
\]
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{} y^{\prime \prime }+a^{2} y = x^{2}+x +1
\]
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{} y^{\prime \prime }+a^{2} y = \cos \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+a^{2} y = \cot \left (a x \right )
\]
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