| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -1\right )
\]
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{} y^{\prime \prime }+6 y^{\prime }+18 y = 2 \operatorname {Heaviside}\left (\pi -t \right )
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{} y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x}
\]
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| \[
{} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u = c \cos \left (\omega t \right )
\]
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| \[
{} x^{\prime \prime }-4 x = t
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{} x^{\prime \prime }-4 x = 4 t^{2}
\]
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{} x^{\prime \prime }+x = t^{2}-2 t
\]
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{} x^{\prime \prime }+x = 3 t^{2}+t
\]
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{} x^{\prime \prime }-x = {\mathrm e}^{-3 t}
\]
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{} x^{\prime \prime }-x = 3 \,{\mathrm e}^{2 t}
\]
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{} x^{\prime \prime }-x = t \,{\mathrm e}^{2 t}
\]
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{} x^{\prime \prime }-3 x^{\prime }-x = t^{2}+t
\]
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| \[
{} x^{\prime \prime }-4 x^{\prime }+13 x = 20 \,{\mathrm e}^{t}
\]
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{} x^{\prime \prime }-x^{\prime }-2 x = 2 t +{\mathrm e}^{t}
\]
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{} x^{\prime \prime }+4 x = \cos \left (t \right )
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| \[
{} x^{\prime \prime }+x = \sin \left (2 t \right )-\cos \left (3 t \right )
\]
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| \[
{} x^{\prime \prime }+2 x^{\prime }+2 x = \cos \left (2 t \right )
\]
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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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| \[
{} x^{\prime \prime }-p \left (t \right ) x = q \left (t \right )
\]
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x = t
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{} t^{2} x^{\prime \prime }+3 t x^{\prime }-3 x = t^{2}
\]
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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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| \[
{} -x^{\prime \prime } = 1-x-x^{2}
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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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| \[
{} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y = f \left (x \right )
\]
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| \[
{} x y^{\prime \prime }+y^{\prime }-\frac {4 y}{x} = x^{3}+x
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| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 6 \left (x^{2}+1\right )^{2}
\]
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{3} \sin \left (x \right )
\]
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{} \left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y = x \left (x^{2}-3 x +1\right )^{2}
\]
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| \[
{} x y^{\prime \prime }-\frac {\left (1-2 x \right ) y^{\prime }}{1-x}+\frac {\left (x^{2}-3 x +1\right ) y}{1-x} = \left (1-x \right )^{2}
\]
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| \[
{} x y^{\prime \prime }-y^{\prime } = 3 x^{2}
\]
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| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x} = 2
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
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{} y^{\prime \prime } = \cos \left (2 x \right )
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{} -y+y^{\prime \prime } = 2 x +{\mathrm e}^{2 x}
\]
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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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{} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y = x^{3}-3 x^{2}+3 x -8
\]
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| \[
{} \left (1-\frac {1}{x}\right ) u^{\prime \prime }+\left (\frac {2}{x}-\frac {2}{x^{2}}-\frac {1}{x^{3}}\right ) u^{\prime }-\frac {u}{x^{4}} = \frac {2}{x}-\frac {2}{x^{2}}-\frac {2}{x^{3}}
\]
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{} \left (x +2\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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{} \frac {{y^{\prime \prime }}^{2}}{{y^{\prime }}^{2}}+\frac {y y^{\prime \prime }}{y^{\prime }}-y^{\prime } = 0
\]
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{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 1
\]
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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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