\[ x \left (y'(x)+\sqrt {y'(x)^2+1}\right )-y(x)=0 \] ✓ Mathematica : cpu = 0.0194125 (sec), leaf count = 37
\[\left \{\left \{y(x)\to -\sqrt {-x \left (x-c_1\right )}\right \},\left \{y(x)\to \sqrt {-x \left (x-c_1\right )}\right \}\right \}\]
✓ Maple : cpu = 0.227 (sec), leaf count = 74
\[ \left \{ 2\,{xy \left ( x \right ) {\it \_C1}{\frac {1}{\sqrt {{\frac { \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) ^{2}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}} \left ( \sqrt {{\frac {{x}^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}y \left ( x \right ) x+ \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2} \right ) ^{-1}}+x=0 \right \} \]