| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }+x+\frac {x^{2}}{3} = 0
\]
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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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| \[
{} t x^{\prime \prime } = t x+1
\]
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| \[
{} t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (4-t \right ) x = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-1\right ) x = 0
\]
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| \[
{} s y^{\prime \prime }+\lambda y = 0
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+\delta \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 a x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \left (a^{2}+9\right ) x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -a x_{3} \left (t \right )-b x_{2} \left (t \right )-c x_{1} \left (t \right )]
\]
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| \[
{} x^{\prime } = \lambda x-x^{3}-x^{5}
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -2 y \left (t \right )-x \left (t \right )^{2}]
\]
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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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| \[
{} y^{\prime } = \frac {x}{y^{2} \sqrt {x^{2}+1}}
\]
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| \[
{} 2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime } = 0
\]
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| \[
{} x +2 y-1+3 \left (2 y+x \right ) y^{\prime } = 0
\]
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| \[
{} x^{2}-x y+y^{2}-y y^{\prime } x = 0
\]
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| \[
{} x^{2}-2 y^{2}+y y^{\prime } x = 0
\]
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| \[
{} y+x y^{\prime }+\frac {y^{3} \left (y-x y^{\prime }\right )}{x} = 0
\]
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| \[
{} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime }+\frac {2 x \sin \left (y\right )+y^{3} {\mathrm e}^{x}}{x^{2} \cos \left (y\right )+3 y^{2} {\mathrm e}^{x}} = 0
\]
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| \[
{} 3 x \left (x y-2\right )+\left (x^{3}+2 y\right ) y^{\prime } = 0
\]
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| \[
{} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} \left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0
\]
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| \[
{} 3 x^{2}+4 x y+\left (2 x^{2}+2 y\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = \frac {2 x y}{-x^{2}+y^{2}}
\]
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| \[
{} y^{\prime } = \frac {x^{2}+y^{2}}{x y}
\]
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| \[
{} 1+3 x \sin \left (y\right )-x^{2} \cos \left (y\right ) y^{\prime } = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = x \,{\mathrm e}^{-x}
\]
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| \[
{} y^{\prime }+\frac {y}{x^{2} y^{2}+x} = \frac {x y^{2}}{x^{2} y^{2}+x}
\]
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| \[
{} 4 x y+3 y^{2}-x +x \left (2 y+x \right ) y^{\prime } = 0
\]
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| \[
{} y \left (x +y+1\right )+x \left (x +3 y+2\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = \frac {-x y+\ln \left (x^{2}\right )}{x^{2}+x \,{\mathrm e}^{y}}
\]
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| \[
{} y^{\prime } = \frac {2 x y}{-x^{2}+y^{2}}
\]
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| \[
{} y^{2}+\left (3 x y-1\right ) y^{\prime } = 0
\]
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| \[
{} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+x y+y^{2}\right ) y^{\prime } = 0
\]
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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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| \[
{} y^{\prime } = 1-y+y^{2} {\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{2 x}+\left (2+\frac {5 \,{\mathrm e}^{x}}{2}\right ) y+y^{2}
\]
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| \[
{} y^{\prime } = 1+x +x^{2} \cos \left (x \right )-\left (1+4 x \cos \left (x \right )\right ) y+2 y^{2} \cos \left (x \right )
\]
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| \[
{} \left (x y^{\prime }-y\right )^{2}-{y^{\prime }}^{2}-1 = 0
\]
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| \[
{} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1 = 0
\]
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| \[
{} y = x y^{\prime }+{y^{\prime }}^{3}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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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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| \[
{} \left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y = x \left (x^{2}-3 x +1\right )^{2}
\]
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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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| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} y^{\left (6\right )}+8 y^{\prime \prime \prime } = a \,{\mathrm e}^{x}
\]
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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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| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y = 0
\]
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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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| \[
{} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+x y+y^{2}\right ) y^{\prime } = 0
\]
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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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| \[
{} y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime } = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\]
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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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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime } = x y^{2}-y^{\prime }
\]
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| \[
{} x^{\prime \prime }-s x = 0
\]
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| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }+x y = x +2
\]
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| \[
{} y^{\prime \prime }+\left (x -1\right ) y = {\mathrm e}^{x}
\]
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| \[
{} \left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y = \frac {4 x^{2}+2 x +10}{x^{4}}
\]
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| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
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| \[
{} \cos \left (x \right ) u^{\prime \prime }+\sin \left (x \right ) u^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) u = 0
\]
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| \[
{} y^{\prime \prime } = y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+\left (-x^{2}+1\right ) y = \frac {-x^{2}+x}{1+x}
\]
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| \[
{} x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y = 0
\]
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