| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 3 t \,{\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }+4 y = 3 \sin \left (2 t \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-t} \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime } = 2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right )
\]
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{} y^{\prime \prime }+y = t \left (1+\sin \left (t \right )\right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = 2 t^{2}+4 t \,{\mathrm e}^{2 t}+t \sin \left (2 t \right )
\]
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{} y^{\prime \prime }+4 y = t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t}
\]
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{} y^{\prime \prime }-3 y^{\prime }-4 y = 2 \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right .
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 2 \cos \left (w t \right )
\]
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{} y^{\prime \prime }+y = 2 \cos \left (w t \right )
\]
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{} y^{\prime \prime }+y = 3 \cos \left (w t \right )
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (\frac {t}{4}\right )
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (6 t \right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\]
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| \[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\]
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| \[
{} y^{\prime \prime }+y = \tan \left (t \right )
\]
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{} y^{\prime \prime }+4 y = 3 \sec \left (2 t \right )^{2}
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\]
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| \[
{} y^{\prime \prime }+4 y = 2 \csc \left (\frac {t}{2}\right )
\]
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{} 4 y^{\prime \prime }+y = 2 \sec \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right )
\]
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{} y^{\prime \prime }+4 y = g \left (t \right )
\]
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{} y^{\prime \prime }+y = g \left (t \right )
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| \[
{} y^{\prime \prime }+2 y^{\prime }-2 y = 0
\]
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| \[
{} 9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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{} 6 y^{\prime \prime }+5 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7
\]
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{} y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime \prime \prime }-6 y = t \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }-12 y = 0
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = t
\]
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| \[
{} y^{\prime \prime }-8 y^{\prime }+25 y = 0
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }+4 y = 0
\]
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{} y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right )
\]
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| \[
{} y^{\prime \prime }+w^{2} y = \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+2 y = \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 18 \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0
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| \[
{} y^{\prime \prime \prime \prime }-y = 0
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{} y^{\prime \prime \prime \prime }-9 y = 0
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+4 y = \sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \operatorname {Heaviside}\left (t -2\right )
\]
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{} y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right )
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\]
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| \[
{} y^{\prime \prime \prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\]
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| \[
{} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\]
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| \[
{} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}
\]
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| \[
{} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
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{} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\]
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{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )
\]
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{} y^{\prime \prime }-y = -20 \delta \left (t -3\right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\]
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{} y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right )
\]
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{} y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\]
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{} y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\]
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| \[
{} y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\]
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{} 2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\]
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{} y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+y = \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+w^{2} y = g \left (t \right )
\]
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{} y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right )
\]
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{} 4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right )
\]
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{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right )
\]
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{} 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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{} y^{\prime \prime \prime \prime }-16 y = g \left (t \right )
\]
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{} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = g \left (t \right )
\]
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