DSolve[Derivative[1][y][x] == (1 + 16*a^2*x^2 - 64*a^3*x^3 - 8*a*x*y[x]^2 + 48*a^2*x^2*y[x]^2 + y[x]^4 - 12*a*x*y[x]^4 + y[x]^6)/y[x],y[x],x]