Still stuck on diffrential equations!

1. The problem statement, all variables and given/known data

let x + y = u and y = uv
Expand dx and dy in terms of du and dv

2. Relevant equations



3. The attempt at a solution

i got this answer:

dy = udv + vdu

and

dx = du - udv - vdu


is this correct?

 

ok thanx
now that makes things harder

we have w=(1 - y e^(y/x+y))dx + (1 + xe^(y/x+y)dy

find an integrating factor 'mu' in terms of u and v such that 'mu'w is exact

after subing that lot in for x and y and dx and dy, and rearranging a little i got this:


'mu' = [ (1+u(1-v)d'mu' ... something long and horrible!

how do i do this?