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Mathematica |
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\[
{} y^{\prime } = x^{2} \sin \left (y\right )
\]
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\[
{} y^{\prime } = \frac {y^{2}}{x -2}
\]
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\[
{} 2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\]
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\[
{} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0
\]
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\[
{} y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0
\]
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\[
{} 2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0
\]
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\[
{} 2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 \cos \left (x \right ) y\right ) y^{\prime } = 0
\]
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\[
{} y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0
\]
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\[
{} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\]
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\[
{} y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0
\]
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\[
{} \left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\]
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\[
{} x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0
\]
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\[
{} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0
\]
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\[
{} \left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\]
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\[
{} x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\]
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\[
{} y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime } = 0
\]
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\[
{} x y^{\prime }+y = \left (x y\right )^{{3}/{2}}
\]
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\[
{} y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\]
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\[
{} y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right .
\]
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\[
{} y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right .
\]
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\[
{} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right .
\]
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\[
{} y^{\prime } = -y^{2}+x y+1
\]
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\[
{} \left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0
\]
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\[
{} 2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0
\]
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\[
{} 3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .
\]
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\[
{} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right .
\]
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\[
{} 5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\]
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\[
{} 4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} \left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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\[
{} \left (2 x +1\right ) y^{\prime \prime }-4 \left (1+x \right ) y^{\prime }+4 y = 0
\]
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\[
{} \left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{2 x}}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 1
\]
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\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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\[
{} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\]
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\[
{} \left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\]
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\[
{} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\]
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\[
{} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\]
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\[
{} \left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\]
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\[
{} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{4 t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t^{2}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{3 t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0]
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x = 0
\]
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\[
{} \left (1+2 t \right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\]
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\[
{} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
\]
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\[
{} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\]
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\[
{} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
\]
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\[
{} f \left (t \right ) x^{\prime \prime }+g \left (t \right ) x = 0
\]
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\[
{} 2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\]
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\[
{} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\]
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\[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{2}]
\]
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\[
{} x^{\prime } = -x \left (k^{2}+x^{2}\right )
\]
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\[
{} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\]
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\[
{} 2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\]
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\[
{} \left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-\sin \left (x \right ) y = 0
\]
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\[
{} {\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
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\[
{} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\]
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\[
{} x^{\prime } = \frac {x^{2}+t \sqrt {x^{2}+t^{2}}}{t x}
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} \left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\]
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\[
{} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\]
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\[
{} x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\]
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\[
{} y^{\prime } = \frac {y}{x +y^{3}}
\]
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\[
{} y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\]
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\[
{} {y^{\prime }}^{2}+y^{2} = 4
\]
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\[
{} y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\]
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\[
{} y^{\prime } = x +y^{2}
\]
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\[
{} y^{\prime } = x y^{3}+x^{2}
\]
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\[
{} y^{\prime } = x^{2}-y^{2}
\]
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\[
{} y = 5 x y^{\prime }-{y^{\prime }}^{2}
\]
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\[
{} y^{\prime } = x -y^{2}
\]
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\[
{} y = x y^{\prime }+{y^{\prime }}^{2}
\]
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\[
{} x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0
\]
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\[
{} \left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
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