\[ x y'(x)^2+\sqrt {y'(x)^2+1}+y(x)=0 \] ✓ Mathematica : cpu = 9.52374 (sec), leaf count = 60
\[\text {Solve}\left [\left \{x=\frac {c_1}{(\text {K$\$$3193905}+1)^2}+\frac {-\sqrt {\text {K$\$$3193905}^2+1}-\sinh ^{-1}(\text {K$\$$3193905})}{(\text {K$\$$3193905}+1)^2},y(x)=\text {K$\$$3193905}^2 (-x)-\sqrt {\text {K$\$$3193905}^2+1}\right \},\{y(x),\text {K$\$$3193905}\}\right ]\] ✓ Maple : cpu = 0.231 (sec), leaf count = 581
\[ \left \{ {{x}^{2}{\it \_C1} \left ( \sqrt {-4\,xy \left ( x \right ) +2+2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}}-2\,x \right ) ^{-2}}+x+2\,{\frac {{x}^{2}}{ \left ( \sqrt {-4\,xy \left ( x \right ) +2+2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}}-2\,x \right ) ^{2}} \left ( \sqrt {2}\sqrt {{\frac {2\,{x}^{2}-2\,xy \left ( x \right ) +\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+1}{{x}^{2}}}}-2\,{\it Arcsinh} \left ( 1/2\,{\frac {\sqrt {-4\,xy \left ( x \right ) +2+2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}}}{x}} \right ) \right ) }=0,{{x}^{2}{\it \_C1} \left ( \sqrt {-4\,xy \left ( x \right ) +2+2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}}+2\,x \right ) ^{-2}}+x+2\,{\frac {{x}^{2}}{ \left ( \sqrt {-4\,xy \left ( x \right ) +2+2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}}+2\,x \right ) ^{2}} \left ( \sqrt {2}\sqrt {{\frac {2\,{x}^{2}-2\,xy \left ( x \right ) +\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+1}{{x}^{2}}}}+2\,{\it Arcsinh} \left ( 1/2\,{\frac {\sqrt {-4\,xy \left ( x \right ) +2+2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}}}{x}} \right ) \right ) }=0,{{x}^{2}{\it \_C1} \left ( \sqrt {-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}-2\,x \right ) ^{-2}}+x+2\,{\frac {{x}^{2}}{ \left ( \sqrt {-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}-2\,x \right ) ^{2}} \left ( -2\,{\it Arcsinh} \left ( 1/2\,{\frac {\sqrt {-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}}{x}} \right ) +\sqrt {{\frac {4\,{x}^{2}-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}{{x}^{2}}}} \right ) }=0,{{x}^{2}{\it \_C1} \left ( \sqrt {-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}+2\,x \right ) ^{-2}}+x+2\,{\frac {{x}^{2}}{ \left ( \sqrt {-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}+2\,x \right ) ^{2}} \left ( 2\,{\it Arcsinh} \left ( 1/2\,{\frac {\sqrt {-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}}{x}} \right ) +\sqrt {{\frac {4\,{x}^{2}-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}{{x}^{2}}}} \right ) }=0 \right \} \]