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Mathematica |
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\[
{}y^{\prime } = \sqrt {x -y}
\] |
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\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0
\] |
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\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime } = 6 x^{4}
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-{\mathrm e}^{t} y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+t^{2} y \left (t \right )-\sin \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right )]
\] |
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\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\] |
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\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x}
\] |
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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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\[
{}x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
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\[
{}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\] |
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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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\[
{}y^{\prime } = {| y|}+1
\] |
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\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{\sin \left (x \right )}
\] |
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\[
{}y^{\prime } = \frac {{\mathrm e}^{x}+y}{x^{2}+y^{2}}
\] |
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\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{\ln \left (x y\right )}
\] |
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\[
{}y^{\prime } = \left (x^{2}+y^{2}\right ) y^{{1}/{3}}
\] |
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\[
{}y^{\prime } = \ln \left (1+x^{2}+y^{2}\right )
\] |
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\[
{}y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
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\[
{}y^{\prime } = \left (x^{2}+y^{2}\right )^{2}
\] |
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\[
{}2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime } = 0
\] |
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\[
{}y \sin \left (x y\right )+x y^{2} \cos \left (x y\right )+\left (x \sin \left (x y\right )+x y^{2} \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} \cos \left (x \right ) y-x^{3} y \sin \left (x \right )+4 x +\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime } = 0
\] |
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\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0
\] |
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\[
{}y^{\prime } = y^{2}+\cos \left (t^{2}\right )
\] |
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\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
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\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
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\[
{}\sqrt {1+y^{2}}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
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\[
{}2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
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\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = t y^{a}
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+2 t
\] |
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\[
{}y^{\prime } = \frac {t^{2}+y^{2}}{1+t +y^{2}}
\] |
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\[
{}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 y \left (t \right )^{2}-3 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -b x \left (t \right ) y \left (t \right )+m, y^{\prime }\left (t \right ) = b x \left (t \right ) y \left (t \right )-g y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right ), z^{\prime }\left (t \right ) = x \left (t \right )+\sin \left (z \left (t \right )\right )]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {\left (x_{1} \left (t \right )^{2}+\sqrt {x_{1} \left (t \right )^{2}+4 x_{2} \left (t \right )^{2}}\right ) x_{1} \left (t \right )}{2}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}+1, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = \tan \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right )+x \left (t \right )^{3}]
\] |
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\[
{}x^{2}+3 x y^{\prime } = y^{3}+2 y
\] |
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\[
{}2 x +y+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
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\[
{}x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime } = 0
\] |
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\[
{}y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}1+x y \left (x y^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0
\] |
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\[
{}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\] |
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\[
{}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
\] |
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\[
{}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\] |
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\[
{}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 y {y^{\prime }}^{2} x^{2} = 0
\] |
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\[
{}x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime } = y
\] |
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\[
{}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1
\] |
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\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
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\[
{}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-\cos \left (t \right ) t\right ]
\] |
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\[
{}y^{2} \left (x^{2}+1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0
\] |
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\[
{}x y y^{\prime } = \left (1+x \right ) \left (1+y\right )
\] |
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\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
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\[
{}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2}
\] |
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\[
{}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0
\] |
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\[
{}{y^{\prime }}^{3}+y^{2} = x y y^{\prime }
\] |
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\[
{}y = x y^{\prime }-x^{2} {y^{\prime }}^{3}
\] |
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\[
{}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2}
\] |
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\[
{}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right )
\] |
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\[
{}2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x = y
\] |
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\[
{}y^{\prime }+f \left (x \right )^{2} = f^{\prime }\left (x \right )+y^{2}
\] |
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\[
{}y^{\prime } = f \left (x \right )+a y+b y^{2}
\] |
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\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+y^{2} a
\] |
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\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2}
\] |
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\[
{}y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
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\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n}
\] |
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\[
{}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\] |
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\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0
\] |
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\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0
\] |
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\[
{}x y^{\prime } = \sin \left (x -y\right )
\] |
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\[
{}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} = 0
\] |
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\[
{}x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\] |
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\[
{}y y^{\prime }+x^{3}+y = 0
\] |
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\[
{}y y^{\prime }+f \left (x \right ) = g \left (x \right ) y
\] |
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\[
{}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0
\] |
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\[
{}x \left (a +y\right ) y^{\prime }+b x +c y = 0
\] |
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