| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }-x = t
\]
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{} x^{\prime \prime }+4 x^{\prime }+x = k
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| \[
{} x^{\prime \prime }-2 x = 2 \,{\mathrm e}^{t}
\]
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| \[
{} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5} = 0
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| \[
{} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x = 0
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| \[
{} x^{\prime \prime }+2 t^{3} x = 0
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| \[
{} x^{\prime \prime }-p \left (t \right ) x = q \left (t \right )
\]
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| \[
{} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0
\]
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| \[
{} x^{\prime \prime }+x^{\prime }+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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| \[
{} 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 }-2 x^{\prime }+x = 0
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| \[
{} x^{\prime \prime }-4 x^{\prime }+3 x = 1
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| \[
{} x^{\prime \prime }+x = g \left (t \right )
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| \[
{} x^{\prime \prime } = \delta \left (-t +a \right )
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| \[
{} x^{\prime \prime }+2 x^{\prime }-x = 0
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| \[
{} x^{\prime \prime }+2 x^{\prime }+x = 0
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| \[
{} x^{\prime \prime }+2 h x^{\prime }+k^{2} x = 0
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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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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2}
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| \[
{} y^{\prime \prime }+b y^{\prime }+c y = f \left (x \right )
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| \[
{} x^{\prime \prime }-4 x = 0
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| \[
{} y^{\prime \prime }-5 y = 0
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 0
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
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| \[
{} x^{\prime \prime } = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }-y = 0
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| \[
{} y^{\prime \prime }+y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
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| \[
{} 5 y+4 y^{\prime }+y^{\prime \prime } = 0
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }-2 y = 0
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| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }+10 y = 0
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| \[
{} y^{\prime \prime }+y^{\prime }-6 y = 0
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| \[
{} y^{\prime \prime }+16 y = 0
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| \[
{} y^{\prime \prime }-6 y^{\prime }+25 y = 0
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| \[
{} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25} = 0
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = \sin \left (x \right )
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| \[
{} y^{\prime \prime } = 9 x^{2}+2 x -1
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = x^{2}+2 x
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = x^{3}+3
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| \[
{} y^{\prime \prime }+y^{\prime }-6 y = 2 x^{3}+5 x^{2}-7 x +2
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (x \right )
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }+4 y = \sin \left (x \right )+\sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 2 \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (x +\frac {\pi }{4}\right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 x^{2}+{\mathrm e}^{x}+2 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right )
\]
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