\[ y'(x)=\frac {48 a^2 x^2 y(x)^2-64 a^3 x^3+16 a^2 x^2-12 a x y(x)^4-8 a x y(x)^2+y(x)^6+y(x)^4+1}{y(x)} \] ✓ Mathematica : cpu = 0.34374 (sec), leaf count = 130
\[\text {Solve}\left [2 a \left (x-\frac {1}{2} \text {RootSum}\left [-48 \text {$\#$1}^2 a^2 y(x)^2+64 \text {$\#$1}^3 a^3-16 \text {$\#$1}^2 a^2+12 \text {$\#$1} a y(x)^4+8 \text {$\#$1} a y(x)^2+2 a-y(x)^6-y(x)^4-1\& ,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 a^2-24 \text {$\#$1} a y(x)^2-8 \text {$\#$1} a+3 y(x)^4+2 y(x)^2}\& \right ]\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 19.054 (sec), leaf count = 75
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {{\it \_a}}{-{{\it \_a}}^{6}+12\,{{\it \_a}}^{4}ax-48\,{{\it \_a}}^{2}{a}^{2}{x}^{2}+64\,{a}^{3}{x}^{3}-{{\it \_a}}^{4}+8\,{{\it \_a}}^{2}ax-16\,{a}^{2}{x}^{2}+2\,a-1}}\,{\rm d}{\it \_a}+x-{\it \_C1}=0 \right \} \]