| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
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{} y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+\cos \left (2 x \right ) {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+4 y = x \sin \left (x \right )
\]
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{} -y+y^{\prime \prime } = x^{2} \cos \left (x \right )
\]
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{} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\]
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| \[
{} 6 y-5 y^{\prime }+y^{\prime \prime } = x +{\mathrm e}^{m x}
\]
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| \[
{} -a^{2} y+y^{\prime \prime } = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\]
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{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
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| \[
{} -y+y^{\prime \prime } = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\]
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{} y^{\prime \prime }-4 y^{\prime }+3 y = \cos \left (2 x \right ) {\mathrm e}^{x}+\cos \left (3 x \right )
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| \[
{} 20 y-9 y^{\prime }+y^{\prime \prime } = 20 x
\]
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{} y^{\prime \prime } = x^{2} \sin \left (x \right )
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| \[
{} y^{\prime \prime } = \frac {a}{x}
\]
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{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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| \[
{} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{4 x}
\]
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| \[
{} -y+y^{\prime \prime } = 5 x +2
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2}
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}}
\]
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{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x}
\]
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| \[
{} y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )+\cos \left (b x \right )
\]
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{} y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right )
\]
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{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
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| \[
{} -y+y^{\prime \prime } = \cosh \left (x \right ) \cos \left (x \right )
\]
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{} y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x}
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| \[
{} y+2 y^{\prime }+y^{\prime \prime } = x \cos \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \sin \left (x \right ) x
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| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right )
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{} y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right )
\]
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{} y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3}
\]
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{} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0
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{} y^{\prime \prime } = x +\sin \left (x \right )
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{} y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime } = \frac {a}{x}
\]
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| \[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y = x
\]
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{} y^{\prime \prime }+y = \csc \left (x \right )
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{} y^{\prime \prime }+4 y = 4 \tan \left (2 x \right )
\]
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| \[
{} -y+y^{\prime \prime } = \frac {2}{{\mathrm e}^{x}+1}
\]
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{} y^{\prime \prime }+n^{2} y = \sec \left (n x \right )
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+y = a \cos \left (2 x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right )
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| \[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
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{} y^{\prime \prime } = x^{2} \sin \left (x \right )
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{} y^{\prime \prime } = \sec \left (x \right )^{2}
\]
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{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
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| \[
{} x^{\prime \prime }-3 x^{\prime }+2 x = 6 \,{\mathrm e}^{3 t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 10
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = 5+10 \sin \left (2 x \right )
\]
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{} 6 y-5 y^{\prime }+y^{\prime \prime } = 3 \,{\mathrm e}^{x}
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{} y^{\prime \prime }+5 y^{\prime }-6 y = 3 \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
\]
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| \[
{} y^{\prime \prime }+y^{\prime } = 3 x^{2}
\]
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{} -y+y^{\prime \prime } = {\mathrm e}^{x}+1
\]
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{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = 6 x \,{\mathrm e}^{2 x}
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{x}\right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 20 \,{\mathrm e}^{-2 x}
\]
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{} y^{\prime \prime }+y = 2 \sin \left (3 x \right )
\]
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{} y^{\prime \prime }+y = 1+2 \cos \left (x \right )
\]
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{} x^{\prime \prime }+x = 5 t^{2}
\]
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{} x^{\prime \prime }+x = 2 \tan \left (t \right )
\]
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| \[
{} y^{\prime \prime }-k^{2} y = f \left (x \right )
\]
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{} -y+y^{\prime \prime } = {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-y = t \,{\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }-3 y^{\prime }-4 y = t^{2}
\]
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{} y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{t}
\]
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{} y^{\prime \prime }+4 y = \delta \left (t -1\right )
\]
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{} 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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