\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-2\,{\frac {a}{-y \left ( x \right ) -2\,a-2\,a \left ( y \left ( x \right ) \right ) ^{4}+16\,{a}^{2}x \left ( y \left ( x \right ) \right ) ^{2}-32\,{a}^{3}{x}^{2}-2\,a \left ( y \left ( x \right ) \right ) ^{6}+24\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}x-96\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{3}{x}^{2}+128\,{a}^{4}{x}^{3}}}=0} \]
Mathematica: cpu = 0.127516 (sec), leaf count = 131 \[ \text {Solve}\left [\frac {\text {RootSum}\left [-64 \text {$\#$1}^3 a^3+48 \text {$\#$1}^2 a^2 y(x)^2+16 \text {$\#$1}^2 a^2-12 \text {$\#$1} a y(x)^4-8 \text {$\#$1} a y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 a^2-24 \text {$\#$1} a y(x)^2-8 \text {$\#$1} a+3 y(x)^4+2 y(x)^2}\& \right ]}{8 a^2}+\frac {y(x)}{2 a}=c_1,y(x)\right ] \]
Maple: cpu = 0.063 (sec), leaf count = 41 \[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}+{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,ax}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}}{8\,{a}^{2}}}-{\it \_C1}=0 \right \} \]