\[ y'(x)=-\frac {8 (a-1) (a+1) x}{a^8 x^6-4 a^6 x^6-3 a^6 x^4 y(x)^2-2 a^6 x^4+6 a^4 x^6+9 a^4 x^4 y(x)^2+6 a^4 x^4+3 a^4 x^2 y(x)^4+4 a^4 x^2 y(x)^2-4 a^2 x^6-9 a^2 x^4 y(x)^2-6 a^2 x^4-6 a^2 x^2 y(x)^4-8 a^2 x^2 y(x)^2-a^2 y(x)^6-2 a^2 y(x)^4-8 a^2+x^6+3 x^4 y(x)^2+2 x^4+3 x^2 y(x)^4+4 x^2 y(x)^2+y(x)^6+2 y(x)^4-8 y(x)+8} \] ✓ Mathematica : cpu = 3.48779 (sec), leaf count = 264
DSolve[Derivative[1][y][x] == (-8*(-1 + a)*(1 + a)*x)/(8 - 8*a^2 + 2*x^4 - 6*a^2*x^4 + 6*a^4*x^4 - 2*a^6*x^4 + x^6 - 4*a^2*x^6 + 6*a^4*x^6 - 4*a^6*x^6 + a^8*x^6 - 8*y[x] + 4*x^2*y[x]^2 - 8*a^2*x^2*y[x]^2 + 4*a^4*x^2*y[x]^2 + 3*x^4*y[x]^2 - 9*a^2*x^4*y[x]^2 + 9*a^4*x^4*y[x]^2 - 3*a^6*x^4*y[x]^2 + 2*y[x]^4 - 2*a^2*y[x]^4 + 3*x^2*y[x]^4 - 6*a^2*x^2*y[x]^4 + 3*a^4*x^2*y[x]^4 + y[x]^6 - a^2*y[x]^6),y[x],x]
\[\text {Solve}\left [\frac {y(x)}{(a-1) (a+1)}-\frac {8 \text {RootSum}\left [-\text {$\#$1}^3 a^6+3 \text {$\#$1}^3 a^4-3 \text {$\#$1}^3 a^2+\text {$\#$1}^3+3 \text {$\#$1}^2 a^4 y(x)^2+2 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2 y(x)^2-4 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2 y(x)^2+2 \text {$\#$1}^2-3 \text {$\#$1} a^2 y(x)^4-4 \text {$\#$1} a^2 y(x)^2+3 \text {$\#$1} y(x)^4+4 \text {$\#$1} y(x)^2+y(x)^6+2 y(x)^4+8\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 a^4-6 \text {$\#$1}^2 a^2+3 \text {$\#$1}^2-6 \text {$\#$1} a^2 y(x)^2-4 \text {$\#$1} a^2+6 \text {$\#$1} y(x)^2+4 \text {$\#$1}+3 y(x)^4+4 y(x)^2}\& \right ]}{(a-1) (a+1) \left (2-2 a^2\right )}=c_1,y(x)\right ]\] ✓ Maple : cpu = 2.365 (sec), leaf count = 80
dsolve(diff(y(x),x) = -8*x*(a-1)*(a+1)/(8-8*y(x)+2*x^4+3*a^4*y(x)^4*x^2-3*a^6*y(x)^2*x^4+9*y(x)^2*a^4*x^4-9*y(x)^2*a^2*x^4-6*y(x)^4*a^2*x^2+4*a^4*y(x)^2*x^2-a^2*y(x)^6+a^8*x^6-4*a^6*x^6+6*a^4*x^6-2*a^2*y(x)^4-2*a^6*x^4+6*a^4*x^4-6*a^2*x^4-4*a^2*x^6-8*y(x)^2*a^2*x^2+y(x)^6+3*x^2*y(x)^4+4*x^2*y(x)^2+3*x^4*y(x)^2-8*a^2+2*y(x)^4+x^6),y(x))
\[\frac {y \left (x \right )}{\left (a -1\right ) \left (a +1\right )}+\frac {4 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{3}+2 \textit {\_Z}^{2}+8\right )}{\sum }\frac {\ln \left (-a^{2} x^{2}+x^{2}+y \left (x \right )^{2}-\textit {\_R} \right )}{3 \textit {\_R}^{2}+4 \textit {\_R}}\right )}{a^{4}-2 a^{2}+1}-c_{1} = 0\]