\[ x \left (y'(x)+\sqrt {y'(x)^2+1}\right )-y(x)=0 \] ✓ Mathematica : cpu = 0.0458822 (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 = 0.283 (sec), leaf count = 74
dsolve(x*((diff(y(x),x)^2+1)^(1/2)+diff(y(x),x))-y(x)=0,y(x))
\[\frac {2 x y \left (x \right ) c_{1}}{\sqrt {\frac {\left (y \left (x \right )^{2}+x^{2}\right )^{2}}{x^{2} y \left (x \right )^{2}}}\, \left (\sqrt {\frac {x^{4}+2 x^{2} y \left (x \right )^{2}+y \left (x \right )^{4}}{x^{2} y \left (x \right )^{2}}}\, x y \left (x \right )+y \left (x \right )^{2}-x^{2}\right )}+x = 0\]