DSolve[Derivative[1][y][x] == (4*(-1 + a)*(1 + a)*x)/(-x^4 + 3*a^2*x^4 - 3*a^4*x^4 + a^6*x^4 + 4*y[x] - 2*x^2*y[x]^2 + 4*a^2*x^2*y[x]^2 - 2*a^4*x^2*y[x]^2 - y[x]^4 + a^2*y[x]^4),y[x],x]