\[ \boxed { \sqrt { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1}+x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) =0} \]
Mathematica: cpu = 6.600838 (sec), leaf count = 60 \[ \text {Solve}\left [\left \{x=\frac {c_1}{(\text {K$\$$1484035}+1)^2}+\frac {-\sqrt {\text {K$\$$1484035}^2+1}-\sinh ^{-1}(\text {K$\$$1484035})}{(\text {K$\$$1484035}+1)^2},y(x)=\text {K$\$$1484035}^2 (-x)-\sqrt {\text {K$\$$1484035}^2+1}\right \},\{y(x),\text {K$\$$1484035}\}\right ] \]
Maple: cpu = 0.156 (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 ( \sqrt {{\frac {4\,{ x}^{2}-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}{{x}^{2}}}}-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 ) \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 ( \sqrt {{\frac {4\,{x}^{2}-4\,xy \left ( x \right ) -2\,\sqrt {4\,{x}^{2}-4\,xy \left ( x \right ) +1}+2}{{x}^{2}}} }+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 ) \right ) }=0 \right \} \]