| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right )
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| \[
{} \frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
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| \[
{} \frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\]
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| \[
{} y^{\prime \prime } = \sin \left (x \right )
\]
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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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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\]
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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3}
\]
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| \[
{} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\]
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| \[
{} y^{\prime \prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\]
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| \[
{} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0
\]
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| \[
{} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\]
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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y
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| \[
{} 2 y^{\prime \prime }+y^{\prime }-y = 0
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\]
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| \[
{} y^{\prime \prime }-y = \frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}}
\]
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| \[
{} y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\]
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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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| \[
{} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y = 0
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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
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| \[
{} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
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| \[
{} x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\]
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| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }-4 y = 0
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
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| \[
{} y^{\prime \prime }-k y = 0
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| \[
{} x y^{\prime \prime }+y^{\prime } = 4 x
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 0
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| \[
{} x y^{\prime \prime }-y^{\prime } = 3 x^{2}
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 0
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 4 x
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| \[
{} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 1
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| \[
{} y^{\prime \prime }-2 y^{\prime } = 6
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{} y^{\prime \prime }-2 y = \sin \left (x \right )
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| \[
{} y^{\prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime } = 4
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{} y^{\prime \prime }-y = \sin \left (x \right )
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| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime } = 6 \,{\mathrm e}^{x}
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| \[
{} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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{} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
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| \[
{} x^{2} y^{\prime \prime }-2 y = 0
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| \[
{} y^{\prime \prime }+y^{\prime }-2 y = 0
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 0
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| \[
{} y^{\prime \prime }+y^{\prime } = 0
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| \[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
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| \[
{} y^{\prime \prime }+y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} x y^{\prime \prime }+3 y^{\prime } = 0
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
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| \[
{} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
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| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
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| \[
{} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
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| \[
{} x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
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| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
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| \[
{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
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| \[
{} 3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime } = 0
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| \[
{} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y = 0
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| \[
{} y^{\prime \prime }+y^{\prime }-6 y = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
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{} y^{\prime \prime }+8 y = 0
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| \[
{} 2 y^{\prime \prime }-4 y^{\prime }+8 y = 0
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{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
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| \[
{} 20 y-9 y^{\prime }+y^{\prime \prime } = 0
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{} 2 y^{\prime \prime }+2 y^{\prime }+3 y = 0
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{} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
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| \[
{} y^{\prime \prime }+y^{\prime } = 0
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| \[
{} y^{\prime \prime }-6 y^{\prime }+25 y = 0
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{} 4 y^{\prime \prime }+20 y^{\prime }+25 y = 0
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| \[
{} 3 y+2 y^{\prime }+y^{\prime \prime } = 0
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{} y^{\prime \prime } = 4 y
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{} 4 y^{\prime \prime }-8 y^{\prime }+7 y = 0
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| \[
{} 2 y^{\prime \prime }+y^{\prime }-y = 0
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| \[
{} 16 y^{\prime \prime }-8 y^{\prime }+y = 0
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }+4 y^{\prime }-5 y = 0
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+5 y = 0
\]
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