\[ x y'(x)^2+\sqrt {y'(x)^2+1}+y(x)=0 \] ✓ Mathematica : cpu = 3.20212 (sec), leaf count = 78
DSolve[y[x] + x*Derivative[1][y][x]^2 + Sqrt[1 + Derivative[1][y][x]^2] == 0,y[x],x]
\[\text {Solve}\left [\left \{x=\frac {\log \left (\sqrt {K[1]^2+1}-K[1]\right )-\sqrt {K[1]^2+1}}{(K[1]+1)^2}+\frac {c_1}{(K[1]+1)^2},y(x)=-x K[1]^2-\sqrt {K[1]^2+1}\right \},\{y(x),K[1]\}\right ]\] ✓ Maple : cpu = 0.44 (sec), leaf count = 581
dsolve((diff(y(x),x)^2+1)^(1/2)+x*diff(y(x),x)^2+y(x)=0,y(x))
\[\frac {x^{2} c_{1}}{{\left (\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}-2 x \right )}^{2}}+x +\frac {2 x^{2} \left (\sqrt {2}\, \sqrt {\frac {2 x^{2}-2 x y \left (x \right )+\sqrt {4 x^{2}-4 x y \left (x \right )+1}+1}{x^{2}}}-2 \,\operatorname {arcsinh}\left (\frac {\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}}{2 x}\right )\right )}{{\left (\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}-2 x \right )}^{2}} = 0\]