| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\]
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{} x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\]
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{} x^{\prime \prime }-4 x = \cos \left (2 t \right )
\]
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{} x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
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{} x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
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{} x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\]
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| \[
{} x^{\prime \prime }-2 x^{\prime } = 4
\]
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{} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
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| \[
{} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
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{} x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\]
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{} x^{\prime \prime }+3025 x = \cos \left (45 t \right )
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{} x^{\prime \prime }+x = \tan \left (t \right )
\]
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{} x^{\prime \prime }-x = t \,{\mathrm e}^{t}
\]
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| \[
{} x^{\prime \prime }-x = \frac {1}{t}
\]
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{} x^{\prime \prime }+x = \frac {1}{t +1}
\]
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{} x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\]
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| \[
{} x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\]
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{} x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\]
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| \[
{} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\]
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{} x^{\prime \prime }+9 x = \sin \left (3 t \right )
\]
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{} x^{\prime \prime }-2 x = 1
\]
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{} x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\]
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| \[
{} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right )
\]
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| \[
{} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\]
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{} x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\]
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| \[
{} x^{\prime \prime }-x = \delta \left (t -5\right )
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| \[
{} x^{\prime \prime }+x = \delta \left (t -2\right )
\]
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{} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\]
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| \[
{} x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\]
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| \[
{} x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
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| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = -8 \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
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| \[
{} 6 y-5 y^{\prime }+y^{\prime \prime } = 2-12 x +6 \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x}
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right )
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{} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right )
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{} y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right )
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| \[
{} -4 y-3 y^{\prime }+y^{\prime \prime } = 16 x -12 \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x}
\]
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{} y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x}
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{} y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11
\]
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{} y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2}
\]
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| \[
{} y^{\prime \prime }+y = x \sin \left (x \right )
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| \[
{} y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right )
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| \[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x}
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| \[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x}
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{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x}
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| \[
{} 16 y+8 y^{\prime }+y^{\prime \prime } = 8 \,{\mathrm e}^{-2 x}
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| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x}
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| \[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x}
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{} y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x}
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{} y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right )
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{} y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}
\]
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| \[
{} -y+y^{\prime \prime } = 3 x^{2} {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right )
\]
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{} y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
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| \[
{} y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x}
\]
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| \[
{} y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right )
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{} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right )
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| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right )
\]
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| \[
{} y^{\prime \prime }+y = \cot \left (x \right )
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{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
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{} y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
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{} y^{\prime \prime }+y = \tan \left (x \right ) \sec \left (x \right )
\]
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{} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-2 x} \sec \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right )
\]
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{} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\]
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{} y^{\prime \prime }+y = \tan \left (x \right )^{3}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{x}+1}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{2 x}+1}
\]
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{} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )+1}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = x \ln \left (x \right )
\]
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| \[
{} y^{\prime \prime }+4 y = 8
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\]
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{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\]
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| \[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\]
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{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\]
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| \[
{} x^{\prime \prime }-4 x = t^{2}
\]
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{} x^{\prime \prime }-4 x^{\prime } = t^{2}
\]
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| \[
{} x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\]
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