| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }+2 x^{\prime }+2 x = \cos \left (2 t \right )
\]
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| \[
{} x^{\prime \prime }+x = t \sin \left (2 t \right )
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| \[
{} x^{\prime \prime }-x^{\prime } = t
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{} x^{\prime \prime }-x = {\mathrm e}^{k t}
\]
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{} x^{\prime \prime }-x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\]
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{} x^{\prime \prime }-3 x^{\prime }+2 x = 3 t \,{\mathrm e}^{t}
\]
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{} x^{\prime \prime }-4 x^{\prime }+3 x = 2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t}
\]
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{} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\]
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{} x^{\prime \prime }+4 x = \sin \left (2 t \right )
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{} x^{\prime \prime }+x = 2 \sin \left (t \right )+2 \cos \left (t \right )
\]
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{} x^{\prime \prime }+9 x = \sin \left (t \right )+\sin \left (3 t \right )
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{} x^{\prime \prime }-x = t
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{} x^{\prime \prime }+4 x^{\prime }+x = k
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{} x^{\prime \prime }-2 x = 2 \,{\mathrm e}^{t}
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{} x^{\prime \prime }-4 x^{\prime }+3 x = 1
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{} x^{\prime \prime }+x = g \left (t \right )
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{} x^{\prime \prime } = \delta \left (-t +a \right )
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2}
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{} y^{\prime \prime }+b y^{\prime }+c y = f \left (x \right )
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{} y^{\prime \prime }-y^{\prime }-2 y = \sin \left (x \right )
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| \[
{} y^{\prime \prime } = 9 x^{2}+2 x -1
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+5 y^{\prime }+6 y = x^{2}+2 x
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = x^{3}+3
\]
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{} y^{\prime \prime }+y^{\prime }-6 y = 2 x^{3}+5 x^{2}-7 x +2
\]
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{} y^{\prime \prime }+y = \sin \left (x \right )
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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{} y^{\prime \prime }+4 y = \sin \left (x \right )+\sin \left (2 x \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+5 y = 2 \cos \left (x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (x +\frac {\pi }{4}\right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 x^{2}+{\mathrm e}^{x}+2 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 3 \,{\mathrm e}^{x}
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \left (x^{2}-1\right ) {\mathrm e}^{2 x}+\left (3 x +4\right ) {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+y^{\prime }+8 y = \left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \sin \left (x \right )
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{} y^{\prime \prime }+y^{\prime }-2 y = 2 x -40 \cos \left (2 x \right )
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 2 \,{\mathrm e}^{x}-10 \sin \left (x \right )
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{} y^{\prime \prime }+5 y^{\prime }+6 y = x^{2}+2 x
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
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{} -y+y^{\prime \prime } = {\mathrm e}^{x}
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{} y^{\prime \prime }+y = \tan \left (x \right ) \sec \left (x \right )
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{} y^{\prime \prime }+4 y = \sec \left (2 x \right )
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{} y^{\prime \prime }+y = \csc \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )
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{} y^{\prime \prime }+y = \tan \left (x \right )
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{} y^{\prime \prime } = \cos \left (2 x \right )
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{} -y+y^{\prime \prime } = 2 x +{\mathrm e}^{2 x}
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{} y^{\prime \prime }-2 y^{\prime }+5 y = 16 x^{3} {\mathrm e}^{3 x}
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{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}+7 x -2
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| \[
{} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = f \left (x \right )
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{} y^{\prime \prime }+y = {\mathrm e}^{2 x}
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{} y^{\prime \prime }+y = \sin \left (x \right )
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| \[
{} y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (x \right )
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{2 x}
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| \[
{} -y+y^{\prime \prime } = x^{2}-x +1
\]
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{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \left (1+x \right )
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{} y^{\prime \prime }+y^{\prime }-12 y = x^{2} {\mathrm e}^{x}
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| \[
{} y^{\prime \prime }+2 b y^{\prime }+y = k
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{} \theta ^{\prime \prime }+4 \theta = 15 \cos \left (3 t \right )
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{} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = t
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{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right .
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{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right .
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{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
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| \[
{} {y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1 = 0
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{} y^{\prime \prime }+y^{\prime } = 6 y+5 \,{\mathrm e}^{2 x}
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{} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
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{} y^{\prime \prime }-y^{\prime } = 6 x^{5} {\mathrm e}^{x}
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = x \,{\mathrm e}^{2 x}
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{} y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )
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| \[
{} y^{\prime \prime }+2 a y^{\prime }+a^{2} y = x^{2} {\mathrm e}^{-a x}
\]
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 2 \,{\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+9 y = 5 \cos \left (2 t \right )
\]
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{} y^{\prime \prime }+y = \sin \left (2 t \right )
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{} y^{\prime \prime }+4 y = t \sin \left (t \right )
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{} y^{\prime \prime }+4 y = x \sin \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0
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{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}}
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{} y^{\prime \prime }+y^{\prime } = \sin \left (2 x \right )
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{} y^{\prime \prime }+4 y = 2 t -8
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{} y^{\prime \prime }+y = 2 \cos \left (t \right )
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| \[
{} y+2 y^{\prime }+y^{\prime \prime } = x
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x}
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{} y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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{} y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime } = 9 x^{2}+2 x -1
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
\]
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