\[ \boxed { \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) ^{2}=0} \]
Mathematica: cpu = 1.402678 (sec), leaf count = 35 \[ \text {DSolve}\left [\left (x y'(x)-y(x)\right ) y''(x)-\left (y'(x)^2+1\right )^2=0,y(x),x\right ] \]
Maple: cpu = 0.265 (sec), leaf count = 66 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {-{\it \_f}+{\it RootOf} \left ( - \tan \left ( {{\it \_Z}}^{-1} \right ) {\it \_C1}\,{\it \_Z}+{\it \_f}\, {\it \_C1}\,\tan \left ( {{\it \_Z}}^{-1} \right ) +\tan \left ( {{\it \_Z}}^{-1} \right ) {\it \_Z}\,{\it \_f}+{\it \_C1}\,{\it \_Z}\,{\it \_f}+\tan \left ( {{\it \_Z}}^{-1} \right ) +{\it \_C1}+{\it \_Z}-{\it \_f} \right ) }{{{\it \_f}}^{2}+1}}{d{\it \_f}}+{\it \_C2} \right ) x \right \} \]