\[ x \left (y'(x)+\sqrt {y'(x)^2+1}\right )-y(x)=0 \] ✓ Mathematica : cpu = 0.0458822 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\sqrt {-x^2+c_1 x}\right \},\left \{y(x)\to \sqrt {-x^2+c_1 x}\right \}\right \}\] ✓ Maple : cpu = 0.283 (sec), leaf count = 74
\[\frac {2 x y \relax (x ) c_{1}}{\sqrt {\frac {\left (y \relax (x )^{2}+x^{2}\right )^{2}}{x^{2} y \relax (x )^{2}}}\, \left (\sqrt {\frac {x^{4}+2 x^{2} y \relax (x )^{2}+y \relax (x )^{4}}{x^{2} y \relax (x )^{2}}}\, x y \relax (x )+y \relax (x )^{2}-x^{2}\right )}+x = 0\]