Homework Help: Differential equations problem

1. Jul 16, 2008

sahen

solve the following ivp
xy' - y = 3xe^2y/x
y(1)=-1

how can i get rid of e ? does anybody help me ?

2. Jul 16, 2008

CompuChip

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. Jul 16, 2008

Defennder

It's hard to read what you wrote. Do you mean: $$xy' - y = \frac{3xe^2y}{x}$$?

4. Jul 17, 2008

sahen

It should be xy' - y = 3xe$$^{2y/x}$$
I guess i need to study more thanks for your help.

5. Jul 17, 2008

CompuChip

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
I'm not even sure there is an exact solution.

6. Jul 17, 2008

crystalplane

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. Jul 17, 2008

Hurkyl

Staff Emeritus
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.

Last edited: Jul 17, 2008
8. Jul 18, 2008

Defennder

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