\[ \boxed { \left ( x\sqrt {{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+1}-y \left ( x \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \sqrt {{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+1}-x \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) =0} \]
Mathematica: cpu = 0.109514 (sec), leaf count = 27 \[ \text {Solve}\left [\sqrt {x^2+y(x)^2+1}+\tan ^{-1}\left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]
Maple: cpu = 0.140 (sec), leaf count = 27 \[ \left \{ \arctan \left ( {\frac {y \left ( x \right ) }{x}} \right ) - \sqrt {{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+1}-{\it \_C1}=0 \right \} \]