DSolve[Derivative[1][y][x] == 1 + x/2 + x^2/4 + x^3/8 - x^4/8 - (3*x^5)/32 - x^6/64 - x*y[x] + (x^2*y[x])/4 + (3*x^3*y[x])/4 + (3*x^4*y[x])/16 + y[x]^2 - (3*x*y[x]^2)/2 - (3*x^2*y[x]^2)/4 + y[x]^3,y[x],x]