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Differential equations problem

  1. Jul 16, 2008 #1
    solve the following ivp
    xy' - y = 3xe^2y/x
    y(1)=-1

    how can i get rid of e ? does anybody help me ?
    thanks in advance.
     
  2. jcsd
  3. Jul 16, 2008 #2

    CompuChip

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    I assume that e is just the Euler number 2.7...
    Why would you want to get rid of it? And why then don't you ask: "how can I get rid of 3?"
     
  4. Jul 16, 2008 #3

    Defennder

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    It's hard to read what you wrote. Do you mean: [tex]xy' - y = \frac{3xe^2y}{x}[/tex]?
     
  5. Jul 17, 2008 #4
    It should be xy' - y = 3xe[tex]^{2y/x}[/tex]
    I guess i need to study more thanks for your help.
     
  6. Jul 17, 2008 #5

    CompuChip

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    Ah, so the equation is
    [tex]
    x y' - y = 3 x \exp\left[ \frac{2y}{x} \right]
    [tex]
    ... that makes the problem significantly more complex :smile:
    I'm not even sure there is an exact solution.
     
  7. Jul 17, 2008 #6
    For the IVP problem, you should find I(X)
    you may get I(x)=e^x dx
    then you multiply I(X) on both sides and you can solve the problem i guess
     
  8. Jul 17, 2008 #7

    Hurkyl

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    On the contrary, it suggests an obvious thing to try. And due to good fortune*, it works.

    Really, this is one of those problems that (at least for the beginner) should fall into the category of "this looks complicated -- there is only one thing I could possibly do, and I just have to hope it works".


    *: Okay, fine, it's more likely that it was rigged to work. :wink:
     
    Last edited: Jul 17, 2008
  9. Jul 18, 2008 #8

    Defennder

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    It takes a substitution to make things a lot easier as Hurkyl said.
     
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