\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {ax}{-{x}^{3}y \left ( x \right ) +2\,a{x}^{3}+2\,a \left ( y \left ( x \right ) \right ) ^{4}{x}^{3}-16\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}{x}^{2}+32\,{a}^{3}x+2\,a \left ( y \left ( x \right ) \right ) ^{6}{x}^{3}-24\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}{x}^{2}+96\, \left ( y \left ( x \right ) \right ) ^{2}x{a}^{3}-128\,{a}^{4}}}=0} \]
Mathematica: cpu = 1.400178 (sec), leaf count = 205 \[ \text {Solve}\left [-\text {RootSum}\left [-\text {$\#$1}^3 y(x)^6-\text {$\#$1}^3 y(x)^4-\text {$\#$1}^3+12 \text {$\#$1}^2 a y(x)^4+8 \text {$\#$1}^2 a y(x)^2-48 \text {$\#$1} a^2 y(x)^2-16 \text {$\#$1} a^2+64 a^3\& ,\frac {\text {$\#$1} \log (x-\text {$\#$1})}{3 \text {$\#$1}^2 y(x)^6+3 \text {$\#$1}^2 y(x)^4+3 \text {$\#$1}^2-24 \text {$\#$1} a y(x)^4-16 \text {$\#$1} a y(x)^2+48 a^2 y(x)^2+16 a^2}\& \right ]-\frac {\text {RootSum}\left [248 \text {$\#$1}^3+2 \text {$\#$1}-1\& ,\text {$\#$1} \log \left (248 \text {$\#$1}^2+186 \text {$\#$1}+29 y(x)^2+11\right )\& \right ]-2 a y(x)}{2 a}=c_1,y(x)\right ] \]
Maple: cpu = 3.026 (sec), leaf count = 43 \[ \left \{ -{\frac {y \left ( x \right ) }{2\,a}}+{\frac {1}{8\,{a}^{2}} \int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,{\frac {a}{x}}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}}-{ \it \_C1}=0 \right \} \]