\[ x y'(x)^2+\sqrt {y'(x)^2+1}+y(x)=0 \] ✓ Mathematica : cpu = 5.32891 (sec), leaf count = 67
\[\text {Solve}\left [\left \{x=\frac {-\sqrt {K[1]^2+1}-\sinh ^{-1}(K[1])}{(K[1]+1)^2}+\frac {c_1}{(K[1]+1)^2},y(x)=-x K[1]^2-\sqrt {K[1]^2+1}\right \},\{y(x),K[1]\}\right ]\] ✓ Maple : cpu = 0.213 (sec), leaf count = 581
\[\left \{\frac {c_{1} x^{2}}{\left (-2 x +\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}\right )^{2}}+\frac {2 \left (-2 \arcsinh \left (\frac {\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}}{2 x}\right )+\sqrt {2}\, \sqrt {\frac {2 x^{2}-2 x y \left (x \right )+\sqrt {4 x^{2}-4 x y \left (x \right )+1}+1}{x^{2}}}\right ) x^{2}}{\left (-2 x +\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}\right )^{2}}+x = 0, \frac {c_{1} x^{2}}{\left (2 x +\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}\right )^{2}}+\frac {2 \left (2 \arcsinh \left (\frac {\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}}{2 x}\right )+\sqrt {2}\, \sqrt {\frac {2 x^{2}-2 x y \left (x \right )+\sqrt {4 x^{2}-4 x y \left (x \right )+1}+1}{x^{2}}}\right ) x^{2}}{\left (2 x +\sqrt {-4 x y \left (x \right )+2+2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}}\right )^{2}}+x = 0, \frac {c_{1} x^{2}}{\left (-2 x +\sqrt {-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}\right )^{2}}+\frac {2 \left (-2 \arcsinh \left (\frac {\sqrt {-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}}{2 x}\right )+\sqrt {\frac {4 x^{2}-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}{x^{2}}}\right ) x^{2}}{\left (-2 x +\sqrt {-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}\right )^{2}}+x = 0, \frac {c_{1} x^{2}}{\left (2 x +\sqrt {-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}\right )^{2}}+\frac {2 \left (2 \arcsinh \left (\frac {\sqrt {-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}}{2 x}\right )+\sqrt {\frac {4 x^{2}-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}{x^{2}}}\right ) x^{2}}{\left (2 x +\sqrt {-4 x y \left (x \right )-2 \sqrt {4 x^{2}-4 x y \left (x \right )+1}+2}\right )^{2}}+x = 0\right \}\]