\[ y'(x)=\frac {-64 a^3 x^3+48 a^2 x^2 y(x)^2+16 a^2 x^2-12 a x y(x)^4-8 a x y(x)^2+y(x)^6+y(x)^4+1}{y(x)} \] ✓ Mathematica : cpu = 0.362563 (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 = 12.383 (sec), leaf count = 75
\[\int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}}{-\textit {\_a}^{6}+12 \textit {\_a}^{4} a x -48 \textit {\_a}^{2} a^{2} x^{2}+64 a^{3} x^{3}-\textit {\_a}^{4}+8 \textit {\_a}^{2} a x -16 a^{2} x^{2}+2 a -1}d \textit {\_a} +x -c_{1} = 0\]