\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a}{x \left ( -xy \left ( x \right ) +2\,ax \left ( y \left ( x \right ) \right ) ^{2}-8\,{a}^{2} \right ) }}=0} \]
Mathematica: cpu = 0.091012 (sec), leaf count = 39 \[ \text {Solve}\left [\frac {y(x)^2 e^{-4 a y(x)}}{8 a}-\frac {e^{-4 a y(x)}}{2 x}=c_1,y(x)\right ] \]
Maple: cpu = 0.218 (sec), leaf count = 28 \[ \left \{ {\it \_C1}+{\frac {-x \left ( y \left ( x \right ) \right ) ^{2} +4\,a}{{{\rm e}^{4\,ay \left ( x \right ) }}x}}=0 \right \} \]