\[ x \left (y'(x)+\sqrt {y'(x)^2+1}\right )-y(x)=0 \] ✓ Mathematica : cpu = 0.0700445 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\sqrt {c_1 x-x^2}\right \},\left \{y(x)\to \sqrt {c_1 x-x^2}\right \}\right \}\] ✓ Maple : cpu = 0.129 (sec), leaf count = 74
\[ \left \{ 2\,{xy \left ( x \right ) {\it \_C1}{\frac {1}{\sqrt {{\frac { \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) ^{2}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}} \left ( \sqrt {{\frac {{x}^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2} \right ) ^{-1}}+x=0 \right \} \]