1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Another 1st order diffy eq.

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]x\frac{dy}{dx} = ye^{\frac{x}{y}} - x[/tex]

    3. The attempt at a solution

    If you divide both sides by x, and substitute u = y/x and y' = u'x + u, we get

    [tex]u'x =ue^{\frac{1}{u}} - u - 1[/tex].

    This is seperable, but how the heck do you integrate the RHS? Or could we just say, like what we do in linear DE's, that

    (ux)' = e^(1/u) - 1, and then integrate both sides? Although unusual, is that correct?
    Last edited: Oct 11, 2008
  2. jcsd
  3. Oct 11, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    How would you integrate e^(1/u)-1 dx without knowing u(x)?!

    Try the substitution u(x)=x/y instead.
  4. Oct 11, 2008 #3
    Still nonelementary. I think there must be a typo in the book because an integral like that is unusual for this class. Heck, maybe it isn't a typo at all because the book is just asking us to classify said differential equation.
  5. Oct 11, 2008 #4


    User Avatar
    Homework Helper
    Gold Member

    Hmmm. yes not easily integrated, but since all you're asked to do is classify the DE, its clearly separable.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Another 1st order diffy eq.
  1. 1st order diff eq. (Replies: 2)

  2. 1st order diff. eq. (Replies: 7)

  3. 1st order dif eq help (Replies: 6)