| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+9 y = \cos \left (3 x \right )-\sin \left (3 x \right )
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{} y^{\prime \prime }-13 y^{\prime }+36 y = x \,{\mathrm e}^{4 x}
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \tan \left (x \right )
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{} y^{\prime \prime }-10 y^{\prime }+25 y = x^{2} {\mathrm e}^{5 x}
\]
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{} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y = x \ln \left (x \right )
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{} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y = 5+3 x
\]
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{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\]
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| \[
{} x y^{\prime \prime }-2 y^{\prime }+\frac {\left (x^{2}+2\right ) y}{x} = 4+\tan \left (x \right )
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{} y^{\prime \prime }+5 y^{\prime } = \sin \left (x \right )
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| \[
{} y^{\prime \prime }+y = x
\]
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{} y^{\prime \prime }-3 y = \cos \left (x \right )
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{} y^{\prime \prime }+2 y = {\mathrm e}^{x}
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{} y^{\prime \prime }-y = {\mathrm e}^{x}
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{} y^{\prime \prime }+y = x +2 \,{\mathrm e}^{-x}
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}+\sin \left (x \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-y = x \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+y = x +{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-y = {\mathrm e}^{x}+\sin \left (x \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-y = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+4 y = 4 x^{3}-8 x^{2}-14 x +7
\]
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{} y^{\prime \prime }+y = {\mathrm e}^{x} \left (1+x \right )
\]
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{} y^{\prime \prime }-y = x \sin \left (x \right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \cos \left (x \right )
\]
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| \[
{} 2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}-1\right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+y = \sin \left (x \right )
\]
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{} y^{\prime \prime }+4 y = \sin \left (x \right )
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 x \,{\mathrm e}^{-x}+x^{2}
\]
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{} y^{\prime \prime }-y = 4 \cosh \left (x \right )
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{} y^{\prime \prime } = 3
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{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = x^{3}
\]
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{} x^{2} y^{\prime \prime }-x y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right )
\]
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{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-7 y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right )
\]
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{} y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }-3 y = {\mathrm e}^{2 x} \left (x +3\right )
\]
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{} y^{\prime \prime }+y = x +2 \,{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-y = x \,{\mathrm e}^{x}
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x}
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
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{} y^{\prime \prime }+y = \frac {1}{x}
\]
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{} y^{\prime \prime }+y = \cos \left (x \right )
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{} y^{\prime \prime }-3 y = x \ln \left (x \right )
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{} 4 y^{\prime \prime }+7 y^{\prime }+3 y = 5 \cos \left (t \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{a x}
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{} y^{\prime \prime }+y = \sin \left (a x \right )
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{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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{} y^{\prime \prime }+y = \sec \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
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{} y^{\prime \prime }+10 y^{\prime }+25 y = \frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}}
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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 }+y = \csc \left (x \right ) \cot \left (x \right )
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{} y^{\prime \prime }-12 y^{\prime }+36 y = {\mathrm e}^{6 x} \ln \left (x \right )
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{} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \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^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{4}}
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{} y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x} \ln \left (x \right )}{x^{2}}
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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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{} 5 x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = \sqrt {x}
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{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = x^{{1}/{4}} \ln \left (x \right )
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{} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime } = \frac {1}{x^{3}}
\]
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{} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y = \frac {\ln \left (x \right )}{x^{2}}
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{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\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 )
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
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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 }+y = \sec \left (x \right )^{3}
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{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{4}}
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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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{} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime } = \frac {1}{x^{3}}
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{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = \left (x^{2}+1\right )^{2}
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| \[
{} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y = {\mathrm e}^{2 x} \left (1-2 x \ln \left (x \right )\right )^{2}
\]
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{} x^{\prime \prime }+2 x^{\prime }+x = -\frac {{\mathrm e}^{-t}}{\left (t +1\right )^{2}}
\]
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{} y^{\prime \prime }+4 y = 4 \cos \left (2 t \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }-4 y = 0
\]
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{} y^{\prime \prime }+2 y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
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{} y^{\prime \prime }-y = 6 \,{\mathrm e}^{t}
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{} y^{\prime \prime }-4 y = -3 \,{\mathrm e}^{t}
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{} y^{\prime \prime }+10 y^{\prime }+25 y = 2 \,{\mathrm e}^{-5 t}
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{} y^{\prime \prime }-9 y^{\prime }+18 y = 54
\]
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{} y^{\prime \prime }-9 y = 20 \cos \left (t \right )
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{} y^{\prime \prime }+9 y = {\mathrm e}^{t}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 24 \cosh \left (t \right )
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{} y^{\prime \prime }+10 y^{\prime }+26 y = 37 \,{\mathrm e}^{t}
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 27 t
\]
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{} y^{\prime \prime }-y^{\prime }-6 y = \cos \left (t \right )+57 \sin \left (t \right )
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{} y^{\prime \prime }-3 y^{\prime }-4 y = 25 t \,{\mathrm e}^{-t}
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{} y^{\prime \prime }+13 y^{\prime }+36 y = 10-72 t
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{} y^{\prime \prime }+2 y^{\prime }-15 y = 16 t \,{\mathrm e}^{-t}-15
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{} y^{\prime \prime }-10 y^{\prime }+21 y = 21 t^{2}+t +13
\]
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{} y^{\prime \prime }+7 y^{\prime }+10 y = 3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t}
\]
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{} 4 y^{\prime \prime }-3 y^{\prime }-y = 34 \sin \left (t \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }-3 y = 3 t^{3}-9 t^{2}-5 t +1
\]
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{} y^{\prime \prime }+4 y^{\prime }+5 y = 39 \,{\mathrm e}^{t} \sin \left (t \right )
\]
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