\[ \boxed { \left ( y \left ( x \right ) f \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) -x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) +xf \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) =0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.218 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}-\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!{\frac {f \left ( {\it \_a} \right ) }{{\it \_a}}}{d{\it \_a}}+2\,{\it \_C1} \right ) \right ) \right ) ^{-1}} \right \} \]