\[ \boxed { f \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) - \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 1.888 (sec), leaf count = 113 \[ \left \{ y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -{\it \_Z}+\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( { \it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!-{\frac {1}{2\,{\it \_a}\, \left ( f \left ( {\it \_a} \right ) -{\it \_a} \right ) }\sqrt {- \left ( f \left ( {\it \_a} \right ) -{\it \_a} \right ) f \left ( {\it \_a} \right ) }}{d{\it \_a}}+{\it \_C1} \right ) \right ) \right ) ^{-1}},y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -{\it \_Z }+\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!{\frac {1}{2\,{\it \_a}\, \left ( f \left ( {\it \_a} \right ) -{\it \_a} \right ) }\sqrt {- \left ( f \left ( {\it \_a} \right ) -{\it \_a} \right ) f \left ( {\it \_a} \right ) }}{d{\it \_a}}+ {\it \_C1} \right ) \right ) \right ) ^{-1}} \right \} \]