\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1+ \left ( y \left ( x \right ) \right ) ^{4}-8\,ax \left ( y \left ( x \right ) \right ) ^{2}+16\,{a}^{2}{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{6}-12\, \left ( y \left ( x \right ) \right ) ^{4}ax+48\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}{x}^{2}-64\,{a}^{3}{x}^{3}}{y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.262533 (sec), leaf count = 130 \[ \text {Solve}\left [2 a \left (x-\frac {1}{2} \text {RootSum}\left [64 \text {$\#$1}^3 a^3-48 \text {$\#$1}^2 a^2 y(x)^2-16 \text {$\#$1}^2 a^2+12 \text {$\#$1} a y(x)^4+8 \text {$\#$1} a y(x)^2+2 a-y(x)^6-y(x)^4-1\& ,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 a^2-24 \text {$\#$1} a y(x)^2-8 \text {$\#$1} a+3 y(x)^4+2 y(x)^2}\& \right ]\right )=c_1,y(x)\right ] \]
Maple: cpu = 0.359 (sec), leaf count = 75 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {{\it \_a}}{-{ {\it \_a}}^{6}+12\,{{\it \_a}}^{4}ax-48\,{{\it \_a}}^{2}{a}^{2}{x}^{2} +64\,{a}^{3}{x}^{3}-{{\it \_a}}^{4}+8\,{{\it \_a}}^{2}ax-16\,{a}^{2}{x }^{2}+2\,a-1}}\,{\rm d}{\it \_a}+x-{\it \_C1}=0 \right \} \]