DSolve[Derivative[1][y][x] == (-2*x - 2*x^3 + x^6 - y[x] - 3*x^2*y[x] + 3*x^5*y[x] - x*y[x]^2 + 3*x^4*y[x]^2 + x^3*y[x]^3)/(x*(1 + x^2 + x*y[x])),y[x],x]