| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 3 y y^{\prime } y^{\prime \prime } = -1+{y^{\prime }}^{3}
\]
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{} \left (x -{y^{\prime }}^{2}\right ) y^{\prime \prime } = x^{2}-y^{\prime }
\]
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{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime } = b
\]
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{} 4 y {y^{\prime }}^{2} y^{\prime \prime } = 3+{y^{\prime }}^{4}
\]
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| \[
{} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime } = 0
\]
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{} {y^{\prime \prime }}^{2} = b y+a
\]
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{} {y^{\prime \prime }}^{2} = a +b {y^{\prime }}^{2}
\]
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| \[
{} a x -2 y^{\prime } y^{\prime \prime }+x {y^{\prime \prime }}^{2} = 0
\]
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{} \left (x y^{\prime \prime }-y^{\prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\]
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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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{} y^{\prime \prime }-5 y^{\prime }+6 y = {\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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{} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\]
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{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3}
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x}
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{} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x}
\]
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| \[
{} y^{3} y^{\prime \prime } = k
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}-1
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
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{} x y^{\prime \prime }-y^{\prime } = x^{2}
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{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
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{} x y^{\prime \prime }-y^{\prime } = x^{2}
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{} y^{\prime \prime }-4 y^{\prime } = 10
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = 16
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{} y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x}
\]
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{} y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x}
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right )
\]
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{} y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
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{} y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right )
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{} 5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right )
\]
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{} y^{\prime \prime }+9 y = 30 \sin \left (3 x \right )
\]
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{} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right )
\]
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{} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right )
\]
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{} y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right )
\]
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{} 5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x
\]
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{} 2 y^{\prime \prime }+y^{\prime } = 2 x
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{} y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }+y = 8 x \sin \left (x \right )
\]
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{} y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x}
\]
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{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5
\]
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{} -y+y^{\prime \prime } = \sinh \left (x \right )
\]
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{} y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right )
\]
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{} y+2 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right )
\]
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{} y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x}
\]
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{} k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}}
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4}
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x}
\]
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{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3}
\]
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right )
\]
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{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x
\]
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