| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+y = \sin \left (x \right )
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{} y^{\prime \prime }+4 y = \cos \left (2 x \right )
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{} y^{\prime \prime }+9 y = {\mathrm e}^{2 x}
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{} y^{\prime \prime }+4 y = {\mathrm e}^{3 x}
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{} 4 y^{\prime \prime }+y = {\mathrm e}^{-2 x}
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{} y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x}
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{} y^{\prime \prime }+4 y = \cos \left (3 x \right )
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{} y^{\prime \prime }+9 y = \cos \left (3 x \right )
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right )
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{} y^{\prime \prime }+36 y = \sin \left (6 x \right )
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{} y^{\prime \prime }+9 y = \sin \left (3 x \right )
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{} y^{\prime \prime }+36 y = \cos \left (6 x \right )
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{} y^{\prime \prime }+3 y^{\prime }-4 y = 12 \,{\mathrm e}^{2 x}
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{} y^{\prime \prime }+3 y^{\prime }-4 y = 21 \,{\mathrm e}^{3 x}
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{} y^{\prime \prime }+3 y^{\prime }-4 y = 15 \,{\mathrm e}^{x}
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{} y^{\prime \prime }+3 y^{\prime }-4 y = 20 \,{\mathrm e}^{-4 x}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}
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{} 4 y^{\prime \prime }-y = {\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{x}
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{} y^{\prime \prime }+16 y = 14 \cos \left (3 x \right )
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{} 4 y^{\prime \prime }+y = 33 \sin \left (3 x \right )
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{} y^{\prime \prime }+16 y = 24 \sin \left (4 x \right )
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{} y^{\prime \prime }+16 y = 48 \cos \left (4 x \right )
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{} y^{\prime \prime }+y = 12 \cos \left (2 x \right )-\sin \left (3 x \right )
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{} y^{\prime \prime }+y = \sin \left (3 x \right )+4 \cos \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (2 x \right ) {\mathrm e}^{x}
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{} y^{\prime \prime }+2 y^{\prime }+5 y = \sin \left (2 x \right ) {\mathrm e}^{-x}
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| \[
{} -y+y^{\prime \prime } = x^{3}
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| \[
{} -y+y^{\prime \prime } = x^{4}
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| \[
{} 4 y^{\prime \prime }+y = x^{3}
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{} 4 y^{\prime \prime }+y = x^{4}
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{} y^{\prime \prime }-2 y^{\prime }+y = x^{2}
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{} y+2 y^{\prime }+y^{\prime \prime } = x^{2}+3 x +3
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{} y^{\prime \prime }-2 y^{\prime }+y = x^{3}-4 x^{2}
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| \[
{} y+2 y^{\prime }+y^{\prime \prime } = x^{3}+6 x^{2}
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 6 x^{2}-6 x -11
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 x^{3}-9 x^{2}+2 x -16
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = 6 x^{2} {\mathrm e}^{2 x}
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| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x}
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| \[
{} y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}
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| \[
{} y^{\prime \prime }+4 y = 8 x^{5}
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{} y^{\prime \prime }+4 y = 16 x \,{\mathrm e}^{2 x}
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{} 5 y+4 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{-2 x} \cos \left (x \right )
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{} y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}-3 \,{\mathrm e}^{-x}
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{} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
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{} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \sin \left (x \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \left (x -2\right ) {\mathrm e}^{x}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 72 x \,{\mathrm e}^{-x}
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{} y^{\prime \prime }+4 y = 12 \sin \left (x \right )+12 \sin \left (2 x \right )
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{} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right )
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| \[
{} y^{\prime \prime }+16 y = 8 x +8 \sin \left (4 x \right )
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{} y^{\prime \prime }+4 y = 8 \cos \left (x \right ) \sin \left (x \right )
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| \[
{} y^{\prime \prime }+4 y = 8 \cos \left (x \right )^{2}
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{} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \cos \left (x \right )
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{} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \cos \left (3 x \right )
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{} y^{\prime \prime }+25 y = \sin \left (5 x \right )
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = x^{2}-2 x
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| \[
{} y^{\prime \prime }+y = 4 \,{\mathrm e}^{x}
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| \[
{} y^{\prime \prime }+4 y = -8+2 x
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 4 x^{2}
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{} -y+y^{\prime \prime } = \sin \left (2 x \right )
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| \[
{} y^{\prime \prime }+2 y^{\prime } = 2 x
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| \[
{} y^{\prime \prime }+2 y^{\prime } = 2 x
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{} y+2 y^{\prime }+y^{\prime \prime } = x +2
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{} y+2 y^{\prime }+y^{\prime \prime } = x +2
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{} y^{\prime \prime }+y = 3
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{} y^{\prime \prime }+y = \csc \left (x \right ) \cot \left (x \right )
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{} y^{\prime \prime }+y = \cot \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
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{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
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{} y^{\prime \prime }+y = \sec \left (x \right )^{4}
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{} y^{\prime \prime }+y = \tan \left (x \right )
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{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
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{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )^{2} \csc \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 }-3 y^{\prime }+2 y = \frac {{\mathrm e}^{2 x}}{{\mathrm e}^{2 x}+1}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right )
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| \[
{} -y+y^{\prime \prime } = \frac {2}{\sqrt {1-{\mathrm e}^{-2 x}}}
\]
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{} -y+y^{\prime \prime } = {\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right )
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{} y^{\prime \prime }-5 y^{\prime }+4 y = \frac {6}{1+{\mathrm e}^{-2 x}}
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{} -y+y^{\prime \prime } = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
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{} y^{\prime \prime }-4 y^{\prime }-3 y = \cos \left ({\mathrm e}^{-x}\right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 15 \sqrt {1+{\mathrm e}^{-x}}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}}
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = f \left (x \right )
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{} y+2 y^{\prime }+y^{\prime \prime } = \frac {1}{\left (-1+{\mathrm e}^{x}\right )^{2}}
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{} y+2 y^{\prime }+y^{\prime \prime } = \frac {1}{\left ({\mathrm e}^{x}+1\right )^{2}}
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{} y^{\prime \prime }-4 y^{\prime }+3 y = \sin \left ({\mathrm e}^{-x}\right )
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{} -y+y^{\prime \prime } = \frac {2 \,{\mathrm e}^{x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
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{} y^{\prime \prime }+y = \sec \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
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{} y^{\prime \prime }+y = \csc \left (x \right )^{3}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}}
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}}
\]
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{} -y+y^{\prime \prime } = \frac {2 \,{\mathrm e}^{-x}}{\left (1+{\mathrm e}^{-2 x}\right )^{2}}
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| \[
{} -y+y^{\prime \prime } = \frac {1}{\left (1-{\mathrm e}^{2 x}\right )^{{3}/{2}}}
\]
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| \[
{} -y+y^{\prime \prime } = {\mathrm e}^{2 x} \left (3 \tan \left ({\mathrm e}^{x}\right )+{\mathrm e}^{x} \sec \left ({\mathrm e}^{x}\right )^{2}\right )
\]
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| \[
{} y^{\prime \prime }+y = \sec \left (x \right )^{2} \tan \left (x \right )
\]
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{} y^{\prime \prime }+y = \csc \left (x \right )
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