| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+a^{2} y = 0
\]
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| \[
{} y^{\prime \prime } = \frac {1}{\sqrt {a y}}
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| \[
{} y^{\prime \prime }+\frac {a^{2}}{y^{2}} = 0
\]
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| \[
{} y^{\prime \prime }-\frac {a^{2}}{y^{2}} = 0
\]
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{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} y^{\prime \prime }-a {y^{\prime }}^{2} = 0
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = \ln \left (y\right ) y^{2}
\]
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| \[
{} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} a^{2} y^{\prime \prime } y^{\prime } = x
\]
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| \[
{} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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| \[
{} y+x y^{\prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\]
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| \[
{} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}
\]
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| \[
{} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
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| \[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\]
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| \[
{} y^{\prime \prime } = \frac {a}{x}
\]
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| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\]
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| \[
{} a y^{\prime \prime } = y^{\prime }
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| \[
{} y^{3} y^{\prime \prime } = a
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| \[
{} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2}
\]
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| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x}
\]
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| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = x
\]
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| \[
{} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
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| \[
{} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0
\]
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| \[
{} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0
\]
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| \[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0
\]
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{} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\]
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{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\]
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| \[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y = 0
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| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
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| \[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\]
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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y
\]
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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0
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{} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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{} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0
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| \[
{} y^{\prime \prime }-2 b y^{\prime }+y b^{2} x^{2} = 0
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| \[
{} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
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| \[
{} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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| \[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\]
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{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\]
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| \[
{} -y+x y^{\prime }+y^{\prime \prime } = f \left (x \right )
\]
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| \[
{} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = x^{3}
\]
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| \[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\]
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{} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
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{} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime } = 0
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| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
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| \[
{} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
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{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{r} = 0
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{} y^{\prime \prime }-n^{2} y = 0
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{} 2 x^{\prime \prime }+5 x^{\prime }-12 x = 0
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{} y^{\prime \prime }+3 y^{\prime }-54 y = 0
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{} 9 x^{\prime \prime }+18 x^{\prime }-16 x = 0
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{} y^{\prime \prime }+2 y^{\prime }+y = 0
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{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
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{} y^{\prime \prime }-y = 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^{\prime \prime }-y = \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^{\prime \prime }+2 y^{\prime }+y = 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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{} y^{\prime \prime }-4 y^{\prime }+4 y = 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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{} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
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{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\]
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{} x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0
\]
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{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
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{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\]
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{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\]
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{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4}
\]
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\]
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{} x^{2} y^{\prime \prime }+2 x y^{\prime } = \ln \left (x \right )
\]
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{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = x
\]
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