\[ \sqrt {x^2+1} (y(x)-x) y'(x)-a \sqrt {\left (y(x)^2+1\right )^3}=0 \] ✗ Mathematica : cpu = 300.043 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 1.788 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( -\arctan \left ( x \right ) +\int ^{-\arctan \left ( x \right ) +{\it \_Z}}\!-{\frac {1}{2\,{a}^{2}+\cos \left ( 2\,{\it \_a} \right ) -1} \left ( \cos \left ( 2\,{\it \_a} \right ) -1-\sqrt {-2\,{a}^{2} \left ( \cos \left ( 2\,{\it \_a} \right ) -1 \right ) } \right ) }{d{\it \_a}}+{\it \_C1} \right ) \right ) \right \} \]