\[ y'(x)=-\frac {8 (a-1) (a+1) x}{a^8 x^6-4 a^6 x^6-3 a^6 x^4 y(x)^2-2 a^6 x^4+6 a^4 x^6+9 a^4 x^4 y(x)^2+6 a^4 x^4+3 a^4 x^2 y(x)^4+4 a^4 x^2 y(x)^2-4 a^2 x^6-9 a^2 x^4 y(x)^2-6 a^2 x^4-6 a^2 x^2 y(x)^4-8 a^2 x^2 y(x)^2-a^2 y(x)^6-2 a^2 y(x)^4-8 a^2+x^6+3 x^4 y(x)^2+2 x^4+3 x^2 y(x)^4+4 x^2 y(x)^2+y(x)^6+2 y(x)^4-8 y(x)+8} \] ✓ Mathematica : cpu = 5.72073 (sec), leaf count = 247
\[\text {Solve}\left [\left (a^2-1\right ) c_1=\frac {4 \text {RootSum}\left [-\text {$\#$1}^3 a^6+3 \text {$\#$1}^3 a^4-3 \text {$\#$1}^3 a^2+\text {$\#$1}^3+3 \text {$\#$1}^2 a^4 y(x)^2+2 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2 y(x)^2-4 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2 y(x)^2+2 \text {$\#$1}^2-3 \text {$\#$1} a^2 y(x)^4-4 \text {$\#$1} a^2 y(x)^2+3 \text {$\#$1} y(x)^4+4 \text {$\#$1} y(x)^2+y(x)^6+2 y(x)^4+8\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2-6 \text {$\#$1} a^2 y(x)^2-4 \text {$\#$1} a^2+6 \text {$\#$1} y(x)^2+4 \text {$\#$1}+3 y(x)^4+4 y(x)^2}\& \right ]}{a^2-1}+y(x),y(x)\right ]\]
✓ Maple : cpu = 4.441 (sec), leaf count = 80
\[ \left \{ {\frac {y \left ( x \right ) }{ \left ( a-1 \right ) \left ( a+1 \right ) }}+4\,{\frac {1}{{a}^{4}-2\,{a}^{2}+1}\sum _{{\it \_R}={\it RootOf} \left ( {{\it \_Z}}^{3}+2\,{{\it \_Z}}^{2}+8 \right ) }{\frac {\ln \left ( -{a}^{2}{x}^{2}+{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_R} \right ) }{3\,{{\it \_R}}^{2}+4\,{\it \_R}}}}-{\it \_C1}=0 \right \} \]