| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right ) \cos \left (y \left (t \right )\right ), y^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right )]
\]
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| \[
{} \left [{\mathrm e}^{t} x^{\prime }\left (t \right ) = \frac {1}{y \left (t \right )}, {\mathrm e}^{t} y^{\prime }\left (t \right ) = \frac {1}{x \left (t \right )}\right ]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}, y^{\prime }\left (t \right ) = -\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2}\right ]
\]
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| \[
{} y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2}
\]
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| \[
{} y^{\prime } = \frac {\sec \left (x \right )^{2}}{y^{3}+1}
\]
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| \[
{} y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\]
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| \[
{} y \ln \left (t \right )+\left (t -3\right ) y^{\prime } = 2 t
\]
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| \[
{} y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\]
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| \[
{} y^{\prime } = \frac {-y+t}{2 t +5 y}
\]
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| \[
{} y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\]
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| \[
{} y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\]
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| \[
{} y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\]
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| \[
{} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\]
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| \[
{} 2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\]
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| \[
{} {\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\]
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| \[
{} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\]
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| \[
{} 2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0
\]
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| \[
{} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\]
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| \[
{} \frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\]
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| \[
{} 2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\]
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| \[
{} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\]
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| \[
{} y y^{\prime } x = \left (x +y\right )^{2}
\]
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| \[
{} y^{\prime } = \frac {4 y-7 x}{5 x -y}
\]
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| \[
{} y^{\prime }+3 t y = 4-4 t^{2}+y^{2}
\]
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| \[
{} x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\]
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| \[
{} y^{\prime }+y-y^{{1}/{4}} = 0
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+x \left (t \right )^{2}, y^{\prime }\left (t \right ) = y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ) x \left (t \right )^{2}-3 x \left (t \right )^{2}-4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) y \left (t \right )^{2}+6 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{4}-\frac {3 x \left (t \right ) y \left (t \right )}{4}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )+2\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ) \left (2-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \left (x \left (t \right )+2\right ) \left (-x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right )\right ]
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\]
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| \[
{} t y^{\prime \prime }+3 y = t
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\]
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| \[
{} t \left (t -4\right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\]
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| \[
{} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right ) = 0
\]
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| \[
{} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\]
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| \[
{} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1} = 0
\]
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| \[
{} y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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| \[
{} y-x y^{\prime }+\left (1-x \cot \left (x \right )\right ) y^{\prime \prime } = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\]
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| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\]
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| \[
{} y^{\prime \prime }+a \left (x y^{\prime }+y\right ) = 0
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = \cosh \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\]
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| \[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\]
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| \[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
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| \[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right )
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = g \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\]
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| \[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
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| \[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y = t
\]
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| \[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\]
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| \[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\]
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| \[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\]
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| \[
{} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }+y \tan \left (x \right ) = 0
\]
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| \[
{} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\]
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| \[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\]
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| \[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\]
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| \[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\]
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| \[
{} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+y \tan \left (x \right ) = 0
\]
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| \[
{} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 1+5 y \left (t \right ), y^{\prime }\left (t \right ) = 1-6 x \left (t \right )^{2}]
\]
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| \[
{} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0
\]
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| \[
{} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\]
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| \[
{} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}}
\]
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| \[
{} y^{\prime } \left (x^{2}+y^{2}+3\right ) = 2 x \left (2 y-\frac {x^{2}}{y}\right )
\]
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| \[
{} y^{\prime } = -x^{2}+y^{2}
\]
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| \[
{} \frac {y y^{\prime }+x}{\sqrt {x^{2}+y^{2}+1}}+\frac {y-x y^{\prime }}{x^{2}+y^{2}} = 0
\]
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| \[
{} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\]
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| \[
{} \frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime } = 0
\]
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| \[
{} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime } = 0
\]
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| \[
{} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0
\]
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| \[
{} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\]
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| \[
{} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3} = 0
\]
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