DSolve[Derivative[1][y][x] == (x*(512 - 256*a*x^2 + 8*a^2*x^8 + a^3*x^12 + 128*a*x^4*y[x] + 24*a^2*x^8*y[x] + 512*y[x]^2 + 192*a*x^4*y[x]^2 + 512*y[x]^3))/512,y[x],x]