| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+\alpha ^{2} y = 1
\]
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| \[
{} y^{\prime } = \frac {y-x}{x +y}
\]
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| \[
{} y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\]
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| \[
{} y^{\prime } = {\mathrm e}^{y}+x y
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )}\right ]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ]
\]
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| \[
{} [x^{\prime \prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right )]
\]
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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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| \[
{} y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right )
\]
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| \[
{} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right )
\]
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| \[
{} y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\]
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| \[
{} y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\]
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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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| \[
{} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\]
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| \[
{} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\]
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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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| \[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\]
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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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| \[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\]
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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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| \[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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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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| \[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\]
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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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| \[
{} y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\]
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| \[
{} y = \frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}}
\]
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| \[
{} y = {y^{\prime }}^{2}-x y^{\prime }+\frac {x^{3}}{2}
\]
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| \[
{} y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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| \[
{} x \left (2 x y+x^{2} y^{\prime }\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 y y^{\prime } x +4 y^{2}-1 = 0
\]
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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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| \[
{} y^{\prime \prime } = x +y^{2}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\]
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| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
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| \[
{} \left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\]
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| \[
{} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\]
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| \[
{} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\]
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| \[
{} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
\]
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| \[
{} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
\]
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| \[
{} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\]
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| \[
{} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\]
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\]
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| \[
{} y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3} = 0
\]
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| \[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\]
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| \[
{} \left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\]
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| \[
{} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0
\]
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| \[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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| \[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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| \[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
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| \[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\]
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| \[
{} y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\]
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| \[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
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| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime } = x y^{2}
\]
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| \[
{} y+x y^{\prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (6 x +3\right ) y^{\prime \prime }+6 y = 0
\]
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| \[
{} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
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| \[
{} y^{\prime }+\frac {y \ln \left (y\right )}{x} = \frac {y}{x^{2}}-\ln \left (y\right )^{2}
\]
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| \[
{} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\]
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| \[
{} x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime } = 0
\]
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| \[
{} x {y^{\prime }}^{2}+a x = 2 y y^{\prime }
\]
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| \[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
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| \[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\]
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| \[
{} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-x y = 0
\]
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| \[
{} \left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right ) = \left (1+y^{\prime }\right )^{2}
\]
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| \[
{} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right )
\]
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| \[
{} y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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| \[
{} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\]
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| \[
{} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}}
\]
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| \[
{} x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0
\]
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| \[
{} x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right ) = 0
\]
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| \[
{} \left (x y \sin \left (x y\right )+\cos \left (x y\right )\right ) y+\left (x y \sin \left (x y\right )-\cos \left (x y\right )\right ) y^{\prime } = 0
\]
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| \[
{} 3 x^{2} y^{4}+2 x y+\left (2 y^{2} x^{3}-x^{2}\right ) y^{\prime } = 0
\]
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| \[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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| \[
{} y^{\prime } = \tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right )
\]
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| \[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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| \[
{} 3 y {y^{\prime }}^{2}-2 y y^{\prime } x +4 y^{2}-x^{2} = 0
\]
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| \[
{} \left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\]
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