\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{x}^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 103.487141 (sec), leaf count = 126 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {x}{c_1 e^{x K[1]}+2 x K[1]+1} \, dK[1]-\int _1^x \left (-\frac {y(x)}{c_1 e^{y(x) K[2]}+2 y(x) K[2]+1}-\frac {c_1 e^{y(x) K[2]}+y(x) K[2]+1}{K[2] \left (c_1 e^{y(x) K[2]}+2 y(x) K[2]+1\right )}+\frac {1}{c_1 e^{K[2]}+2 K[2]+1}\right ) \, dK[2]=c_2,y(x)\right ] \]
Maple: cpu = 0.094 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}{\it RootOf} \left ( -\ln \left ( x \right ) +{\it \_C2}+\int ^{{\it \_Z}}\!- \left ( {{\rm e}^{{ \it \_f}}}{\it \_C1}-2\,{\it \_f}-1 \right ) ^{-1}{d{\it \_f}} \right ) } \right \} \]