\[ y'(x)=-\frac {8 (a-1) (a+1) x}{-3 a^6 x^4 y(x)^2+3 a^4 x^2 y(x)^4+9 a^4 x^4 y(x)^2+4 a^4 x^2 y(x)^2-6 a^2 x^2 y(x)^4-9 a^2 x^4 y(x)^2-8 a^2 x^2 y(x)^2+a^8 x^6-4 a^6 x^6-2 a^6 x^4+6 a^4 x^6+6 a^4 x^4-4 a^2 x^6-6 a^2 x^4-a^2 y(x)^6-2 a^2 y(x)^4-8 a^2+3 x^2 y(x)^4+3 x^4 y(x)^2+4 x^2 y(x)^2+x^6+2 x^4+y(x)^6+2 y(x)^4-8 y(x)+8} \] ✓ Mathematica : cpu = 4.34243 (sec), leaf count = 264
\[\text {Solve}\left [\frac {y(x)}{(a-1) (a+1)}-\frac {8 \text {RootSum}\left [3 \text {$\#$1}^2 a^4 y(x)^2-6 \text {$\#$1}^2 a^2 y(x)^2-\text {$\#$1}^3 a^6+3 \text {$\#$1}^3 a^4+2 \text {$\#$1}^2 a^4-3 \text {$\#$1}^3 a^2-4 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^3+2 \text {$\#$1}^2-3 \text {$\#$1} a^2 y(x)^4-4 \text {$\#$1} a^2 y(x)^2+3 \text {$\#$1} y(x)^4+4 \text {$\#$1} y(x)^2+y(x)^6+2 y(x)^4+8\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2-6 \text {$\#$1} a^2 y(x)^2-4 \text {$\#$1} a^2+6 \text {$\#$1} y(x)^2+4 \text {$\#$1}+3 y(x)^4+4 y(x)^2}\& \right ]}{(a-1) (a+1) \left (2-2 a^2\right )}=c_1,y(x)\right ]\] ✓ Maple : cpu = 2.414 (sec), leaf count = 80
\[ \left \{ {\frac {y \left ( x \right ) }{ \left ( a-1 \right ) \left ( a+1 \right ) }}+4\,{\frac {1}{{a}^{4}-2\,{a}^{2}+1}\sum _{{\it \_R}={\it RootOf} \left ( {{\it \_Z}}^{3}+2\,{{\it \_Z}}^{2}+8 \right ) }{\frac {\ln \left ( -{a}^{2}{x}^{2}+{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_R} \right ) }{3\,{{\it \_R}}^{2}+4\,{\it \_R}}}}-{\it \_C1}=0 \right \} \]