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Homework Help: Still stuck on diffrential equations!

  1. Apr 15, 2008 #1
    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?
     
  2. jcsd
  3. Apr 15, 2008 #2
    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.
     
  4. Apr 15, 2008 #3
    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?
     
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