\[ \left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)-\sqrt {x^2+y(x)^2+1} y(x)-x \left (x^2+y(x)^2\right )=0 \] ✓ Mathematica : cpu = 0.415714 (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 = 0.222 (sec), leaf count = 27
\[\left \{-c_{1}+\arctan \left (\frac {y \left (x \right )}{x}\right )-\sqrt {x^{2}+y \left (x \right )^{2}+1} = 0\right \}\]