\[ x \left (y'(x)+\sqrt {y'(x)^2+1}\right )-y(x)=0 \] ✓ Mathematica : cpu = 0.0320678 (sec), leaf count = 39
DSolve[-y[x] + x*(Derivative[1][y][x] + Sqrt[1 + Derivative[1][y][x]^2]) == 0,y[x],x]
\[\left \{\left \{y(x)\to -\sqrt {-x^2+c_1 x}\right \},\left \{y(x)\to \sqrt {-x^2+c_1 x}\right \}\right \}\] ✓ Maple : cpu = 0.063 (sec), leaf count = 105
dsolve(x*((diff(y(x),x)^2+1)^(1/2)+diff(y(x),x))-y(x)=0,y(x))
\[y \left (x \right ) = \frac {x \left (\sqrt {-\frac {c_{1}^{2}}{x \left (-2 c_{1}+x \right )}}\, \sqrt {-x^{2}+2 x c_{1}}+c_{1}-x \right )}{\sqrt {-x^{2}+2 x c_{1}}}\]