Differential equations problem

  • Thread starter sahen
  • Start date
  • #1
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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.
 

Answers and Replies

  • #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?"
 
  • #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]?
 
  • #4
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It should be xy' - y = 3xe[tex]^{2y/x}[/tex]
I guess i need to study more thanks for your help.
 
  • #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.
 
  • #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
 
  • #7
Hurkyl
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... that makes the problem significantly more complex :smile:.
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:
  • #8
Defennder
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It takes a substitution to make things a lot easier as Hurkyl said.
 

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