| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\]
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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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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x}
\]
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| \[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2} = 0
\]
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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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| \[
{} x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\]
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| \[
{} y^{\prime \prime } \cos \left (x \right )+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y = 2 \cos \left (x \right )^{5}
\]
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| \[
{} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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| \[
{} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y = x^{2}
\]
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| \[
{} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0
\]
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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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| \[
{} y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-y \cot \left (x \right ) = \sin \left (x \right )^{2}
\]
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| \[
{} 3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime } = 0
\]
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| \[
{} y = x y^{\prime }+\frac {1}{y^{\prime }}
\]
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| \[
{} x^{2}-x y+y^{2}-y y^{\prime } x = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
\]
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| \[
{} x y^{\prime \prime }-x y^{\prime }+y = {\mathrm e}^{x}
\]
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| \[
{} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime } = \cos \left (y\right )
\]
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| \[
{} x^{\prime } = x^{3}+a x^{2}-b x
\]
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| \[
{} y^{\prime } = \frac {1+y}{x +2}-{\mathrm e}^{\frac {1+y}{x +2}}
\]
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| \[
{} y^{\prime } = \frac {1+y}{x +2}+{\mathrm e}^{\frac {1+y}{x +2}}
\]
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| \[
{} y^{\prime } = \frac {x +y+1}{x +2}-{\mathrm e}^{\frac {x +y+1}{x +2}}
\]
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| \[
{} \cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime } = 0
\]
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| \[
{} y = x y^{\prime }-\sqrt {y^{\prime }-1}
\]
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| \[
{} y = x {y^{\prime }}^{2}+\ln \left ({y^{\prime }}^{2}\right )
\]
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| \[
{} x = y \left (y^{\prime }+\frac {1}{y^{\prime }}\right )+{y^{\prime }}^{5}
\]
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| \[
{} y^{\prime } = y^{3}+x^{3}
\]
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| \[
{} y^{\prime } = x +\sqrt {1+y^{2}}
\]
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| \[
{} [x^{\prime }\left (t \right ) = \left (3 t -1\right ) x \left (t \right )-\left (1-t \right ) y \left (t \right )+t \,{\mathrm e}^{t^{2}}, y^{\prime }\left (t \right ) = -\left (t +2\right ) x \left (t \right )+\left (t -2\right ) y \left (t \right )-{\mathrm e}^{t^{2}}]
\]
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| \[
{} \left [w_{1}^{\prime }\left (z \right ) = w_{2} \left (z \right ), w_{2}^{\prime }\left (z \right ) = \frac {a w_{1} \left (z \right )}{z^{2}}\right ]
\]
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| \[
{} z^{2} u^{\prime \prime }+\left (3 z +1\right ) u^{\prime }+u = 0
\]
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| \[
{} x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5} = 0
\]
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| \[
{} t^{2} x^{\prime }-2 t x = t^{5}
\]
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| \[
{} x^{\prime } = t +x^{2}
\]
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| \[
{} x^{\prime } = \frac {3 x^{{1}/{3}}}{2}
\]
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| \[
{} x^{\prime } = \sqrt {1-x^{2}}
\]
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| \[
{} x^{\prime } = x^{{1}/{4}}
\]
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| \[
{} x^{\prime } = \sin \left (x\right )
\]
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| \[
{} x^{\prime } = t^{2} x^{4}+1
\]
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| \[
{} x^{\prime } = 2+\sin \left (x\right )
\]
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| \[
{} x^{\prime } = \sin \left (t x\right )
\]
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| \[
{} x^{\prime } = \arctan \left (x\right )+t
\]
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| \[
{} x^{\prime } = x^{2}-t^{2}
\]
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| \[
{} x^{\prime } = x^{2}-1
\]
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| \[
{} x^{\prime } = 5 t \sqrt {x}
\]
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| \[
{} x^{\prime } = 4 t^{3} \sqrt {x}
\]
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| \[
{} a \,x^{p}+b y+\left (b x +d y^{q}\right ) y^{\prime } = 0
\]
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| \[
{} 3 x^{2}-y+\left (4 y^{3}-x \right ) y^{\prime } = 0
\]
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| \[
{} y-x^{{1}/{3}}+\left (x +y\right ) y^{\prime } = 0
\]
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| \[
{} {\mathrm e}^{x}-\frac {y^{2}}{2}+\left ({\mathrm e}^{y}-x y\right ) y^{\prime } = 0
\]
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| \[
{} x^{2}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\]
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| \[
{} x^{2}+2 x y+2 y^{2}+\left (x^{2}+4 x y+5 y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime } = 0
\]
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| \[
{} x^{2}+a_{1} x y+a_{2} y^{2}+\left (x^{2}+y b_{1} x +b_{2} y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} y^{2}+\left (x y+3 y^{3}\right ) y^{\prime } = 0
\]
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| \[
{} {x^{\prime }}^{2} = x^{2}+t^{2}-1
\]
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| \[
{} {x^{\prime }}^{2}-t x+x = 0
\]
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| \[
{} x = t x^{\prime }+\frac {1}{x^{\prime }}
\]
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| \[
{} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0
\]
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| \[
{} x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x = 0
\]
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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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| \[
{} x^{\prime \prime }-\frac {t x^{\prime }}{4}+x = 0
\]
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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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| \[
{} x^{\prime \prime }-t x^{\prime }+3 x = 0
\]
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| \[
{} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x = 0
\]
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| \[
{} x^{\prime \prime \prime }-3 x^{\prime }+k x = 0
\]
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| \[
{} x^{\left (5\right )}+x = 0
\]
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| \[
{} [x^{\prime }\left (t \right )-t y \left (t \right ) = 1, y^{\prime }\left (t \right )-t x^{\prime }\left (t \right ) = 3]
\]
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| \[
{} [t^{2} x^{\prime }\left (t \right )-y \left (t \right ) = 1, y^{\prime }\left (t \right )-2 x \left (t \right ) = 0]
\]
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| \[
{} [t x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = 1, y^{\prime }\left (t \right )+x \left (t \right )+{\mathrm e}^{x^{\prime }\left (t \right )} = 1]
\]
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| \[
{} [x \left (t \right ) x^{\prime }\left (t \right )+y \left (t \right ) = 2 t, y^{\prime }\left (t \right )+2 x \left (t \right )^{2} = 1]
\]
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| \[
{} L x^{\prime \prime }+g \sin \left (x\right ) = 0
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 x \left (t \right ) y \left (t \right )-a x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+4 x \left (t \right ) y \left (t \right )-a y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-4 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (3-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (x \left (t \right )-5\right )]
\]
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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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