Still stuck on diffrential equations!

[sara_87]

1. Homework Statement

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

2. Homework Equations



3. The Attempt at a Solution

i got this answer:

dy = udv + vdu

and

dx = du - udv - vdu


is this correct?

 

[steelphantom]

Looks correct to me. Using the product rule on "y = uv", you get dy, and then a simple substitution in the equation "x + y = u" gives you dx. You got it.

 

[sara_87]

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?