| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0
\]
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| \[
{} x^{\prime \prime }-\frac {t x^{\prime }}{4}+x = 0
\]
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| \[
{} x^{\prime \prime }-\frac {x^{\prime }}{t} = 0
\]
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| \[
{} x^{\prime \prime }-2 x^{\prime } \left (x-1\right ) = 0
\]
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| \[
{} x^{\prime \prime } = 2 {x^{\prime }}^{3} x
\]
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| \[
{} x x^{\prime \prime }-2 {x^{\prime }}^{2}-x^{2} = 0
\]
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| \[
{} x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2} = 0
\]
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| \[
{} x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2} = 0
\]
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| \[
{} t^{2} x^{\prime \prime }-2 x = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+a t x^{\prime }+x = 0
\]
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| \[
{} t^{2} x^{\prime \prime }-t x^{\prime }-3 x = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x = t
\]
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| \[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }-3 x = t^{2}
\]
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| \[
{} x^{\prime \prime }-t x^{\prime }+3 x = 0
\]
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| \[
{} t^{3} x^{\prime \prime \prime }+4 t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\]
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| \[
{} L x^{\prime \prime }+g \sin \left (x\right ) = 0
\]
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| \[
{} x^{\prime \prime } = x-x^{3}
\]
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| \[
{} x^{\prime \prime } = x^{3}-x
\]
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| \[
{} x^{\prime \prime } = x^{3}-x
\]
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| \[
{} x^{\prime \prime } = x^{3}-x
\]
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| \[
{} x^{\prime \prime } = x-x^{3}
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| \[
{} x^{\prime \prime } = x-x^{3}
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| \[
{} x^{\prime \prime } = x-x^{3}
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| \[
{} x^{\prime \prime }+x+8 x^{7} = 0
\]
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| \[
{} x^{\prime \prime }+x+\frac {x^{2}}{3} = 0
\]
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| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
\]
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| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
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| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
\]
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| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x t^{2} = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-1\right ) x = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+\left (-m^{2}+t^{2}\right ) x = 0
\]
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| \[
{} s y^{\prime \prime }+\lambda y = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x t^{2} = \lambda x
\]
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| \[
{} x^{\prime \prime }-x^{3} = 0
\]
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| \[
{} x^{\prime \prime }+4 x^{3} = 0
\]
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| \[
{} x^{\prime \prime }+6 x^{5} = 0
\]
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| \[
{} x^{\prime \prime }+\lambda x-x^{3} = 0
\]
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| \[
{} x^{\prime \prime }+4 x^{3} = 0
\]
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| \[
{} x^{\prime \prime }+4 x^{3} = 0
\]
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| \[
{} -x^{\prime \prime } = 1-x-x^{2}
\]
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| \[
{} -x^{\prime \prime }+x = {\mathrm e}^{-x}
\]
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| \[
{} -x^{\prime \prime }+x = {\mathrm e}^{-x^{2}}
\]
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| \[
{} -x^{\prime \prime } = \frac {1}{\sqrt {1+x^{2}}}-x
\]
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| \[
{} -x^{\prime \prime } = 2 x-x^{2}
\]
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| \[
{} -x^{\prime \prime } = \arctan \left (x\right )
\]
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| \[
{} x u^{\prime \prime }-\left (x^{2} {\mathrm e}^{x}+1\right ) u^{\prime }-x^{2} {\mathrm e}^{x} u = 0
\]
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| \[
{} u^{\prime \prime }-\left (1+x \right ) u^{\prime }+\left (x -1\right ) u = 0
\]
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| \[
{} u^{\prime \prime }+\left (\tan \left (x \right )-2 \cos \left (x \right )\right ) u^{\prime } = 0
\]
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| \[
{} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y = f \left (x \right )
\]
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| \[
{} x y^{\prime \prime }+y^{\prime }-\frac {4 y}{x} = x^{3}+x
\]
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| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 6 \left (x^{2}+1\right )^{2}
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{3} \sin \left (x \right )
\]
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| \[
{} \left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y = x \left (x^{2}-3 x +1\right )^{2}
\]
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| \[
{} x y^{\prime \prime }-\frac {\left (1-2 x \right ) y^{\prime }}{1-x}+\frac {\left (x^{2}-3 x +1\right ) y}{1-x} = \left (1-x \right )^{2}
\]
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| \[
{} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 4 \ln \left (x \right )
\]
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| \[
{} x y^{\prime \prime }-y^{\prime } = 3 x^{2}
\]
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| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x} = 2
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0
\]
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| \[
{} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y = x^{3}-3 x^{2}+3 x -8
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\]
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| \[
{} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0
\]
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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y = 0
\]
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| \[
{} x^{2} \cos \left (x \right ) y^{\prime \prime }+\left (x \sin \left (x \right )-2 \cos \left (x \right )\right ) \left (x y^{\prime }-y\right ) = 0
\]
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| \[
{} \left (1-\frac {1}{x}\right ) u^{\prime \prime }+\left (\frac {2}{x}-\frac {2}{x^{2}}-\frac {1}{x^{3}}\right ) u^{\prime }-\frac {u}{x^{4}} = \frac {2}{x}-\frac {2}{x^{2}}-\frac {2}{x^{3}}
\]
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| \[
{} x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\]
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| \[
{} \left (x +2\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} \frac {{y^{\prime \prime }}^{2}}{{y^{\prime }}^{2}}+\frac {y y^{\prime \prime }}{y^{\prime }}-y^{\prime } = 0
\]
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| \[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 1
\]
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| \[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0
\]
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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 x y = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} x y^{\prime \prime }-{y^{\prime }}^{3}-y^{\prime } = 0
\]
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| \[
{} y^{\prime } = x y^{\prime \prime }+{y^{\prime \prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = {y^{\prime }}^{2}
\]
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{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
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| \[
{} y^{\prime \prime }-\frac {2 {y^{\prime }}^{2}}{y}-y = 0
\]
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| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} x^{\prime \prime } = 4 x^{3}-4 x
\]
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{} x^{\prime \prime }+\sin \left (x\right ) = 0
\]
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| \[
{} x^{\prime \prime } = x^{2}-4 x+\lambda
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 16 x^{3}
\]
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{} y^{\prime \prime \prime }-5 x y^{\prime } = {\mathrm e}^{x}+1
\]
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| \[
{} t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t} = t^{2}-t +1
\]
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| \[
{} s^{2} t^{\prime \prime }+s t t^{\prime } = s
\]
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| \[
{} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5} = p
\]
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| \[
{} y y^{\prime \prime } = 1+y^{2}
\]
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| \[
{} {y^{\prime \prime }}^{2}-3 y y^{\prime }+x y = 0
\]
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| \[
{} x^{4} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} t^{2} s^{\prime \prime }-t s^{\prime } = 1-\sin \left (t \right )
\]
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| \[
{} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+\sin \left (y\right ) = 0
\]
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| \[
{} {r^{\prime \prime }}^{2}+r^{\prime \prime }+y r^{\prime } = 0
\]
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| \[
{} {y^{\prime \prime }}^{{3}/{2}}+y = x
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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| \[
{} 2 x y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0
\]
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