| # | ODE | Mathematica | Maple | Sympy |
| \[
{} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = t^{4}
\]
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| \[
{} t y^{\prime \prime }-y^{\prime } = 3 t^{2}-1
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }+y = t
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}+1}
\]
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| \[
{} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y = t
\]
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| \[
{} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y = t^{2} {\mathrm e}^{-t}
\]
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| \[
{} t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 4 t^{5}
\]
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| \[
{} y^{\prime \prime }-y = \frac {1}{1+{\mathrm e}^{-t}}
\]
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| \[
{} y^{\prime \prime }+a^{2} y = f \left (t \right )
\]
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| \[
{} y^{\prime \prime }-a^{2} y = f \left (t \right )
\]
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| \[
{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = f \left (t \right )
\]
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| \[
{} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y = f \left (t \right )
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -3\right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right .
\]
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✓ |
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| \[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t -3\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime \prime }-y = \delta \left (t -1\right )-\delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 3 \delta \left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 3 \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime \prime }-y = \delta \left (t -1\right )-\delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = \delta \left (t -3\right )
\]
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| \[
{} y^{\prime \prime }+9 y = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }+4 y = 0
\]
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