\[ \boxed { f \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) \sqrt { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1}-x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) =0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 1.919 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}+\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!{\frac {f \left ( {\it \_a} \right ) }{{\it \_a}}{\frac {1}{\sqrt {- \left ( f \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_a}}}}}{d{\it \_a}}+2\,{\it \_C1} \right ) \right ) \right ) ^{-1}} \right \} \]