The solution of the  differential equation is (x+y) dy/dx = 1 is-

x+y+1 = Ce^y

The given differential equation is (x+y) dy/dx = 1

⇒ dy/dx = 1/(x+y)

⇒ dx/dy -x = y

 which is of the form dx/dy + px =Q (Where p= -1 and Q= y)

Now, I.F. = e^∫pdy I.F. = e^∫-dy So. I.F. = e^-y.

The solution is given by:

x.(I.F.) = ∫Q x(I.F.)dy +C

⇒ x.e^-y = ∫(y x e^-y) dy +C

so. x = -y -1 +C^ey

⇒ x+y+1 = Ce^y