\[ x \left (y'(x)+\sqrt {y'(x)^2+1}\right )-y(x)=0 \] ✓ Mathematica : cpu = 0.0489829 (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 = 0.26 (sec), leaf count = 74
\[\left \{\frac {2 c_{1} x y \left (x \right )}{\sqrt {\frac {\left (x^{2}+y \left (x \right )^{2}\right )^{2}}{x^{2} y \left (x \right )^{2}}}\, \left (-x^{2}+\sqrt {\frac {x^{4}+2 x^{2} y \left (x \right )^{2}+y \left (x \right )^{4}}{x^{2} y \left (x \right )^{2}}}\, x y \left (x \right )+y \left (x \right )^{2}\right )}+x = 0\right \}\]