\[ \left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)-\sqrt {x^2+y(x)^2+1} y(x)-x \left (x^2+y(x)^2\right )=0 \] ✓ Mathematica : cpu = 0.337253 (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 = 0.138 (sec), leaf count = 27
\[ \left \{ \arctan \left ( {\frac {y \left ( x \right ) }{x}} \right ) -\sqrt {{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+1}-{\it \_C1}=0 \right \} \]