\[ y'(x)=-\frac {8 (a-1) (a+1) x}{a^8 x^6-4 a^6 x^6-3 a^6 x^4 y(x)^2-2 a^6 x^4+6 a^4 x^6+9 a^4 x^4 y(x)^2+6 a^4 x^4+3 a^4 x^2 y(x)^4+4 a^4 x^2 y(x)^2-4 a^2 x^6-9 a^2 x^4 y(x)^2-6 a^2 x^4-6 a^2 x^2 y(x)^4-8 a^2 x^2 y(x)^2-a^2 y(x)^6-2 a^2 y(x)^4-8 a^2+x^6+3 x^4 y(x)^2+2 x^4+3 x^2 y(x)^4+4 x^2 y(x)^2+y(x)^6+2 y(x)^4-8 y(x)+8} \] ✓ Mathematica : cpu = 4.92098 (sec), leaf count = 264
\[\text {Solve}\left [\frac {y(x)}{(a-1) (a+1)}-\frac {8 \text {RootSum}\left [-\text {$\#$1}^3 a^6+3 \text {$\#$1}^3 a^4-3 \text {$\#$1}^3 a^2+\text {$\#$1}^3+3 \text {$\#$1}^2 a^4 y(x)^2+2 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2 y(x)^2-4 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2 y(x)^2+2 \text {$\#$1}^2-3 \text {$\#$1} a^2 y(x)^4-4 \text {$\#$1} a^2 y(x)^2+3 \text {$\#$1} y(x)^4+4 \text {$\#$1} y(x)^2+y(x)^6+2 y(x)^4+8\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2-6 \text {$\#$1} a^2 y(x)^2-4 \text {$\#$1} a^2+6 \text {$\#$1} y(x)^2+4 \text {$\#$1}+3 y(x)^4+4 y(x)^2}\& \right ]}{(a-1) (a+1) \left (2-2 a^2\right )}=c_1,y(x)\right ]\] ✓ Maple : cpu = 2.188 (sec), leaf count = 80
\[\left \{-c_{1}+\frac {4 \ln \left (-a^{2} x^{2}+x^{2}+y \left (x \right )^{2}-\RootOf \left (\textit {\_Z}^{3}+2 \textit {\_Z}^{2}+8\right )\right )}{\left (a^{4}-2 a^{2}+1\right ) \left (3 \RootOf \left (\textit {\_Z}^{3}+2 \textit {\_Z}^{2}+8\right )^{2}+4 \RootOf \left (\textit {\_Z}^{3}+2 \textit {\_Z}^{2}+8\right )\right )}+\frac {y \left (x \right )}{\left (a -1\right ) \left (a +1\right )} = 0\right \}\]