\[ \boxed { \left ( {\it b2}\,y \left ( x \right ) +{\it a2}\,x+{\it c2} \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( {\it a1}\,x+{\it b1}\,y \left ( x \right ) +{\it c1} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{\it a0}\,x+{\it b0}\,y \left ( x \right ) +{\it c0}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.811 (sec), leaf count = 929 \[ \left \{ x-{{\rm e}^{\int ^{{\frac {1}{2\,{\it b2}\,y \left ( x \right ) +2\,{\it a2}\,x+2\,{\it c2}} \left ( -{\it a1}\,x-{\it b1}\,y \left ( x \right ) -{\it c1}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}-4\, {\it a0}\,{\it b2}\,xy \left ( x \right ) +{{\it a1}}^{2}{x}^{2}+2\,{ \it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) -4\,{\it b0}\,{\it b2}\, \left ( y \left ( x \right ) \right ) ^{2}+{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4 \,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0} \,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\, y \left ( x \right ) -4\,{\it b2}\,{\it c0}\,y \left ( x \right ) -4\,{ \it c0}\,{\it c2}+{{\it c1}}^{2}} \right ) }}\!{\frac {{{\it \_a}}^{2}{ \it a1}\,{\it b2}-{{\it \_a}}^{2}{\it a2}\,{\it b1}+2\,{\it \_a}\,{ \it a0}\,{\it b2}-2\,{\it \_a}\,{\it a2}\,{\it b0}+{\it a0}\,{\it b1}- {\it a1}\,{\it b0}}{ \left ( {{\it \_a}}^{3}{\it b2}+{{\it \_a}}^{2}{ \it a2}+{{\it \_a}}^{2}{\it b1}+{\it \_a}\,{\it a1}+{\it \_a}\,{\it b0 }+{\it a0} \right ) \left ( {{\it \_a}}^{2}{\it b2}+{\it \_a}\,{\it b1} +{\it b0} \right ) }}{d{\it \_a}}}} \left ( \int ^{{\frac {1}{2\,{\it b2 }\,y \left ( x \right ) +2\,{\it a2}\,x+2\,{\it c2}} \left ( -{\it a1}\,x -{\it b1}\,y \left ( x \right ) -{\it c1}+\sqrt {-4\,{\it a0}\,{\it a2} \,{x}^{2}-4\,{\it a0}\,{\it b2}\,xy \left ( x \right ) +{{\it a1}}^{2}{x }^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0 }\,xy \left ( x \right ) -4\,{\it b0}\,{\it b2}\, \left ( y \left ( x \right ) \right ) ^{2}+{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{ \it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{ \it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it b2}\,{\it c0}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}} \right ) }}\!- {\frac {{{\it \_b}}^{2}{\it b1}\,{\it c2}-{{\it \_b}}^{2}{\it b2}\,{ \it c1}+2\,{\it \_b}\,{\it b0}\,{\it c2}-2\,{\it \_b}\,{\it b2}\,{\it c0}+{\it b0}\,{\it c1}-{\it b1}\,{\it c0}}{ \left ( {{\it \_b}}^{2}{ \it b2}+{\it \_b}\,{\it b1}+{\it b0} \right ) \left ( {{\it \_b}}^{3}{ \it b2}+{{\it \_b}}^{2}{\it a2}+{{\it \_b}}^{2}{\it b1}+{\it \_b}\,{ \it a1}+{\it \_b}\,{\it b0}+{\it a0} \right ) }{{\rm e}^{-\int \!{ \frac {{{\it \_b}}^{2}{\it a1}\,{\it b2}-{{\it \_b}}^{2}{\it a2}\,{ \it b1}+2\,{\it \_b}\,{\it a0}\,{\it b2}-2\,{\it \_b}\,{\it a2}\,{\it b0}+{\it a0}\,{\it b1}-{\it a1}\,{\it b0}}{ \left ( {{\it \_b}}^{2}{ \it b2}+{\it \_b}\,{\it b1}+{\it b0} \right ) \left ( {{\it \_b}}^{3}{ \it b2}+{{\it \_b}}^{2}{\it a2}+{{\it \_b}}^{2}{\it b1}+{\it \_b}\,{ \it a1}+{\it \_b}\,{\it b0}+{\it a0} \right ) }}\,{\rm d}{\it \_b}}}}{d {\it \_b}}+{\it \_C1} \right ) =0,x-{{\rm e}^{\int ^{-{\frac {1}{2\,{ \it b2}\,y \left ( x \right ) +2\,{\it a2}\,x+2\,{\it c2}} \left ( {\it a1}\,x+{\it b1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x }^{2}-4\,{\it a0}\,{\it b2}\,xy \left ( x \right ) +{{\it a1}}^{2}{x}^{2 }+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,x y \left ( x \right ) -4\,{\it b0}\,{\it b2}\, \left ( y \left ( x \right ) \right ) ^{2}+{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4 \,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0} \,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\, y \left ( x \right ) -4\,{\it b2}\,{\it c0}\,y \left ( x \right ) -4\,{ \it c0}\,{\it c2}+{{\it c1}}^{2}}+{\it c1} \right ) }}\!{\frac {{{\it \_a}}^{2}{\it a1}\,{\it b2}-{{\it \_a}}^{2}{\it a2}\,{\it b1}+2\,{\it \_a}\,{\it a0}\,{\it b2}-2\,{\it \_a}\,{\it a2}\,{\it b0}+{\it a0}\,{ \it b1}-{\it a1}\,{\it b0}}{ \left ( {{\it \_a}}^{3}{\it b2}+{{\it \_a} }^{2}{\it a2}+{{\it \_a}}^{2}{\it b1}+{\it \_a}\,{\it a1}+{\it \_a}\,{ \it b0}+{\it a0} \right ) \left ( {{\it \_a}}^{2}{\it b2}+{\it \_a}\,{ \it b1}+{\it b0} \right ) }}{d{\it \_a}}}} \left ( \int ^{-{\frac {1}{2 \,{\it b2}\,y \left ( x \right ) +2\,{\it a2}\,x+2\,{\it c2}} \left ( { \it a1}\,x+{\it b1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2} \,{x}^{2}-4\,{\it a0}\,{\it b2}\,xy \left ( x \right ) +{{\it a1}}^{2}{x }^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0 }\,xy \left ( x \right ) -4\,{\it b0}\,{\it b2}\, \left ( y \left ( x \right ) \right ) ^{2}+{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{ \it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{ \it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it b2}\,{\it c0}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}+{\it c1} \right ) }}\!-{\frac {{{\it \_b}}^{2}{\it b1}\,{\it c2}-{{\it \_b}}^{2 }{\it b2}\,{\it c1}+2\,{\it \_b}\,{\it b0}\,{\it c2}-2\,{\it \_b}\,{ \it b2}\,{\it c0}+{\it b0}\,{\it c1}-{\it b1}\,{\it c0}}{ \left ( {{ \it \_b}}^{2}{\it b2}+{\it \_b}\,{\it b1}+{\it b0} \right ) \left ( {{ \it \_b}}^{3}{\it b2}+{{\it \_b}}^{2}{\it a2}+{{\it \_b}}^{2}{\it b1}+ {\it \_b}\,{\it a1}+{\it \_b}\,{\it b0}+{\it a0} \right ) }{{\rm e}^{- \int \!{\frac {{{\it \_b}}^{2}{\it a1}\,{\it b2}-{{\it \_b}}^{2}{\it a2}\,{\it b1}+2\,{\it \_b}\,{\it a0}\,{\it b2}-2\,{\it \_b}\,{\it a2} \,{\it b0}+{\it a0}\,{\it b1}-{\it a1}\,{\it b0}}{ \left ( {{\it \_b}}^ {2}{\it b2}+{\it \_b}\,{\it b1}+{\it b0} \right ) \left ( {{\it \_b}}^{ 3}{\it b2}+{{\it \_b}}^{2}{\it a2}+{{\it \_b}}^{2}{\it b1}+{\it \_b}\, {\it a1}+{\it \_b}\,{\it b0}+{\it a0} \right ) }}\,{\rm d}{\it \_b}}}}{ d{\it \_b}}+{\it \_C1} \right ) =0 \right \} \]