\[ \boxed { {x}^{4}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{x}^{2} \left ( x+{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +4\, \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 283.320477 (sec), leaf count = 166 \[ \text {Solve}\left [\int _1^{y(x)} \frac {1}{c_1 x^2 \left (-e^{\frac {K[1]}{x^2}}\right )+4 K[1]+2 x^2} \, dK[1]-\int _1^x \left (\frac {K[2] \left (c_1 e^{\frac {y(x)}{K[2]^2}}+2 \left (-\frac {y(x)}{K[2]^2}-1\right )\right )}{c_1 K[2]^2 \left (-e^{\frac {y(x)}{K[2]^2}}\right )+2 K[2]^2+4 y(x)}+2 \left (\frac {y(x)}{K[2]^3 \left (c_1 e^{\frac {y(x)}{K[2]^2}}-2\right )-4 y(x) K[2]}+\frac {1}{K[2]^3 \left (2-c_1 e^{\frac {1}{K[2]^2}}\right )+4 K[2]}\right )\right ) \, dK[2]=c_2,y(x)\right ] \]
Maple: cpu = 1.638 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +{\it \_C2}-\int ^{{\it \_Z}}\! \left ( {{\rm e}^{{\it \_f}}}{ \it \_C1}+4\,{\it \_f}+2 \right ) ^{-1}{d{\it \_f}} \right ) {x}^{2} \right \} \]