| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\]
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{} y^{\prime \prime }+4 y = 8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\]
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{} y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime \prime } = x +\sin \left (x \right )
\]
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| \[
{} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x}
\]
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| \[
{} y^{\prime \prime }+y = a x
\]
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{} y^{\prime \prime }+y = a \cos \left (b x \right )
\]
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{} y^{\prime \prime }+y = 8 \cos \left (x \right ) \cos \left (2 x \right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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{} y^{\prime \prime }+y = a \sin \left (b x \right )
\]
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{} y^{\prime \prime }+y = \sin \left (a x \right ) \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }+y = x \left (\cos \left (x \right )-x \sin \left (x \right )\right )
\]
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{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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{} y^{\prime \prime }+y = {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{x} \left (x^{2}-1\right )
\]
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{} y^{\prime \prime }+y = \sin \left (2 x \right ) {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{2 x} \cos \left (x \right )
\]
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| \[
{} -2 y+y^{\prime \prime } = 4 x^{2} {\mathrm e}^{x^{2}}
\]
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| \[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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| \[
{} -a^{2} y+y^{\prime \prime } = 1+x
\]
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| \[
{} y^{\prime \prime } = a x +b y
\]
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| \[
{} y^{\prime \prime }+a^{2} y = x^{2}+x +1
\]
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{} y^{\prime \prime }+a^{2} y = \cos \left (b x \right )
\]
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{} y^{\prime \prime }+a^{2} y = \cot \left (a x \right )
\]
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{} y^{\prime \prime }+a^{2} y = \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \left (x -6\right ) x^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \left (3 x^{2}+2 x +1\right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\]
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| \[
{} y+2 y^{\prime }+y^{\prime \prime } = 3 \,{\mathrm e}^{2 x}+x^{2}-\cos \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 8 x^{2} {\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 50 \cosh \left (x \right ) \cos \left (x \right )
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x} \cos \left (x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \sinh \left (x \right )
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| \[
{} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x \tan \left (a \right )} x^{2}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (a x \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}+\sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x}+x^{2}
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{a x} x
\]
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{} -4 y-3 y^{\prime }+y^{\prime \prime } = 10 \cos \left (2 x \right )
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x} \cos \left (x \right )^{2}
\]
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{} 5 y+4 y^{\prime }+y^{\prime \prime } = \sin \left (x \right )
\]
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{} 6 y-5 y^{\prime }+y^{\prime \prime } = 4 x^{2} {\mathrm e}^{x}
\]
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{} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{a x}
\]
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{} y^{\prime \prime }+6 y^{\prime }+9 y = \cosh \left (x \right ) {\mathrm e}^{-3 x}
\]
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| \[
{} 12 y-7 y^{\prime }+y^{\prime \prime } = x
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{} 16 y+8 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x}
\]
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{} 20 y-9 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{3 x}
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| \[
{} y b^{2}+2 a y^{\prime }+y^{\prime \prime } = c \sin \left (k x \right )
\]
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{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x}
\]
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| \[
{} b y+a y^{\prime }+y^{\prime \prime } = f \left (x \right )
\]
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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 = 12 \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )
\]
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{} y^{\prime \prime }+y^{\prime }+y = x^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right )
\]
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{} y^{\prime \prime }+y^{\prime } = x^{2}+2 x
\]
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{} y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right )
\]
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{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2}
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
\]
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{} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\]
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{} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right )
\]
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{} y^{\prime \prime }+9 y = 8 \cos \left (x \right )
\]
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{} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \left (2 x -3\right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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{} y^{\prime \prime }+y = \cot \left (x \right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
\]
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{} -y+y^{\prime \prime } = \sin \left (x \right )^{2}
\]
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{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x} \ln \left (x \right )
\]
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{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{-x}}{x}
\]
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{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right )
\]
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