DSolve[Derivative[1][y][x] == (alpha^3 + alpha*beta^2*x^2 + beta^3*x^3 + 2*alpha^2*beta*x*y[x] + 3*alpha*beta^2*x^2*y[x] + alpha^3*y[x]^2 + 3*alpha^2*beta*x*y[x]^2 + alpha^3*y[x]^3)/alpha^3,y[x],x]