| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
\]
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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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| \[
{} 2 y-3 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x}
\]
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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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| \[
{} y-2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \ln \left (x \right )
\]
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| \[
{} 2 y-3 y^{\prime }+y^{\prime \prime } = \cos \left ({\mathrm e}^{-x}\right )
\]
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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^{\prime \prime } = 2 y y^{\prime }
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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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| \[
{} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\]
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| \[
{} r^{\prime \prime } = -\frac {k}{r^{2}}
\]
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| \[
{} y^{\prime \prime } = \frac {3 k y^{2}}{2}
\]
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| \[
{} y^{\prime \prime } = 2 k y^{3}
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
\]
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| \[
{} r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}}
\]
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| \[
{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
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| \[
{} y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (1+y^{\prime }\right ) x = 0
\]
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{} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
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| \[
{} 2 y^{\prime \prime } = {\mathrm e}^{y}
\]
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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 y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
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| \[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\]
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| \[
{} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
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| \[
{} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\]
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| \[
{} a x y^{3}+b y^{2}+y^{\prime } = 0
\]
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| \[
{} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0
\]
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| \[
{} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {f \left (x \right ) a +b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0
\]
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| \[
{} x^{2} y^{\prime }+x y^{3}+a y^{2} = 0
\]
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| \[
{} \left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\]
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| \[
{} y^{\prime }+y \tan \left (x \right ) = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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| \[
{} \left (-x^{2}+1\right ) {y^{\prime }}^{2}+1 = 0
\]
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| \[
{} y^{\prime } = {\mathrm e}^{a x}+a y
\]
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| \[
{} \left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2}
\]
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| \[
{} x \left (1-y\right ) y^{\prime }+\left (1+x \right ) y = 0
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{} y^{\prime } = a x y^{2}
\]
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| \[
{} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\]
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| \[
{} x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\]
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| \[
{} \frac {x}{1+y} = \frac {y y^{\prime }}{1+x}
\]
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| \[
{} y^{\prime }+b^{2} y^{2} = a^{2}
\]
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| \[
{} y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\]
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| \[
{} \sin \left (x \right ) \cos \left (y\right ) = \cos \left (x \right ) \sin \left (y\right ) y^{\prime }
\]
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| \[
{} a x y^{\prime }+2 y = y y^{\prime } x
\]
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| \[
{} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+x y = 0
\]
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| \[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}
\]
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| \[
{} x y^{\prime \prime }+2 y^{\prime }+a^{3} x^{2} y = 2
\]
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| \[
{} y^{\prime \prime }+a \,x^{2} y = 1+x
\]
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| \[
{} x^{4} y^{\prime \prime }+x y^{\prime }+y = 0
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| \[
{} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0
\]
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{} \left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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| \[
{} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
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{} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
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| \[
{} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (-n +1\right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (-n +1\right ) x y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0
\]
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{} \left (a^{2}+x^{2}\right ) y^{\prime \prime }+x y^{\prime }-n^{2} y = 0
\]
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| \[
{} a^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
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| \[
{} x y^{\prime \prime }+y^{\prime }+y = 0
\]
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| \[
{} x y^{\prime \prime }+y^{\prime }+p x y = 0
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| \[
{} y+x y^{\prime \prime } = 0
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{} x^{3} y^{\prime \prime }-\left (2 x -1\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0
\]
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{} \left (-x^{2}+x \right ) y^{\prime \prime }-y = 0
\]
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{} x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-x y = 0
\]
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{} y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0
\]
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{} x \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } \left (-x^{2}+1\right )+x y = 0
\]
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{} 4 \left (1-x \right ) x y^{\prime \prime }-4 y^{\prime }-y = 0
\]
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