Partial differential equation?

Question

solve (d denotes the partial derivate)
(x+y)(du/dx - du/dy) = u with condition u(1+s,1 -2s) =1
where s is a constant and u = u(x,y)

Answer 1

I don't know if I ever did these. I've been trying a bit of guess and check, and found that if u = x(x+y) then the sum of the two partial derivatives is x+y, but I guess that's not much help.

I've found out also that if u = x/(x+y) then
[meaning partial derivatives]
du/dx - du/dy = u/x, which looks a little closer but still isn't there.
Interestingly, I think u = x/ (x+y)^2 satisfies the same equation.

Hope you get a solution and I see it!