Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Existence of integrating factor

  1. Sep 6, 2009 #1
    During one lecture it was mentioned that equations of the form P(x,y)dx+Q(x,y)dy=0 always have at least one integrating factor. But the lecturer didn't know the proof, I've tried using Google but no luck. Anybody can show me the proof? Thanks a lot.
     
  2. jcsd
  3. Sep 6, 2009 #2
    If you know a solution of the differential equation dy/dx -P/Q, you can use that to find an integrating factor. Or, if you know an integrating factor you can solve the DE. Sometimes it is easy to find an integrating factor. But usually it is just as hard as solving the DE.
    In any case, what you are looking for is just the existence theorem for solutions to a first-order DE.
     
  4. Sep 7, 2009 #3
    If it is true that there always exist the integrating [tex]\mu(x)[/tex], finding one is not easy. We need to solve
    [tex]\frac{\partial}{\partial y}\mu(x,y)P(x,y) = \frac{\partial}{\partial x}\mu(x,y)Q(x,y) [/tex]

    I agree with g_edgar sometime it just easier to obtain the solution compare to finding the integrating factor.
     
  5. Sep 7, 2009 #4
    Well, thanks man.It seems to be a easy transformation of the question, why didn't I think this way? Kind of embarrassing.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Existence of integrating factor
  1. Integration Factors (Replies: 3)

  2. Integrating Factors (Replies: 1)

  3. Integrating factor (Replies: 1)

  4. Integrating Factor (Replies: 4)

  5. Integrating factor (Replies: 1)

Loading...