\[ \boxed { \left ( y \left ( x \right ) -x \right ) \sqrt {{x}^{2}+1}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a\sqrt { \left ( \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) ^{3}}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 1.045 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( -\arctan \left ( x \right ) +\int ^{-\arctan \left ( x \right ) +{\it \_Z}}\!-{ \frac {1}{2\,{a}^{2}+\cos \left ( 2\,{\it \_a} \right ) -1} \left ( \cos \left ( 2\,{\it \_a} \right ) -1+\sqrt {-2\,{a}^{2}\cos \left ( 2\,{\it \_a} \right ) +2\,{a}^{2}} \right ) }{d{\it \_a}}+{\it \_C1} \right ) \right ) \right \} \]