| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \sec \left ({\mathrm e}^{-x}\right )^{2}
\]
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| \[
{} -y+y^{\prime \prime } = \frac {2}{{\mathrm e}^{x}+1}
\]
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| \[
{} -y+y^{\prime \prime } = \frac {2}{{\mathrm e}^{x}-{\mathrm e}^{-x}}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\]
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| \[
{} -y+y^{\prime \prime } = \frac {1}{{\mathrm e}^{2 x}+1}
\]
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| \[
{} y^{\prime \prime }+y = \sec \left (x \right )^{3} \tan \left (x \right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \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^{\prime \prime }+y = \csc \left (x \right )^{3} \cot \left (x \right )
\]
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| \[
{} y^{\prime \prime } = 2 t +1
\]
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{} y^{\prime \prime } = 6 \sin \left (3 t \right )
\]
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{} y^{\prime \prime } = 6 \sin \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }+4 y = 8
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 9 \,{\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }-5 y = 150 t
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = 4 \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t}
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = 4 \cos \left (2 t \right )
\]
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 50 \sin \left (t \right )
\]
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{} y^{\prime \prime }+4 y = \sin \left (3 t \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = 2 \cos \left (t \right )+\sin \left (t \right )
\]
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{} y^{\prime \prime }+y = 4 \sin \left (t \right )
\]
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{} y^{\prime \prime }+9 y = 36 t \sin \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }-3 y = 4 t^{2} \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+4 y = 32 t \cos \left (2 t \right )
\]
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{} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{t}
\]
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{} y^{\prime \prime }+2 y^{\prime }+3 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+8 y = t
\]
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{} y^{\prime \prime }+2 = \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{t}
\]
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
\]
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{} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-3 t}
\]
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{} y^{\prime \prime }+4 y = 1+{\mathrm e}^{t}
\]
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{} y^{\prime \prime }-y = t^{2}
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{t}
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }+y = 2 \sin \left (t \right )
\]
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t}
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{-3 t}
\]
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{} y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 t} \cos \left (2 t \right )
\]
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{} y^{\prime \prime }-8 y^{\prime }+25 y = 104 \sin \left (3 t \right )
\]
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{} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 t}
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime }-4 y = 2-8 t
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{} y^{\prime \prime }-4 y = {\mathrm e}^{-6 t}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 16 \,{\mathrm e}^{t}
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{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 t}
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
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| \[
{} y^{\prime \prime }+2 y^{\prime }-8 y = 6 \,{\mathrm e}^{-4 t}
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{} y^{\prime \prime }+3 y^{\prime }-10 y = \sin \left (t \right )
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t}
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{} y^{\prime \prime }-5 y^{\prime }-6 y = 10 t \,{\mathrm e}^{4 t}
\]
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{} y^{\prime \prime }-8 y^{\prime }+25 y = 36 t \,{\mathrm e}^{4 t} \sin \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \cos \left (t \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{t} \cos \left (t \right )
\]
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{} y^{\prime \prime }+y^{\prime }+y = t^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }-2 y = \frac {t^{2}+1}{-t^{2}+1}
\]
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{} y^{\prime \prime }+y = \sin \left (t \right )
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{} y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{-3 t}
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{3 t}
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{} y^{\prime \prime }+y = \tan \left (t \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t}
\]
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{} y^{\prime \prime }+y = \sec \left (t \right )
\]
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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 }-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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| \[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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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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