What will be the sufficient condition for the differential equation $M(x,y)\,dx + N(x,y)\,dy =0$ to have an integrating factor as a function of $(x+y).$ What will be integrating factor in that case?
I got struck at $ \frac{ f(x+y)}{f'(x+y)} = \frac{(dM/dy - dN/dx)}{(N-M)}$. How to proceed further??