# Differential equations problem

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

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

CompuChip
Homework Helper
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?"

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

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

CompuChip
Homework Helper
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.

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

Hurkyl
Staff Emeritus
Gold Member
... that makes the problem significantly more complex .
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:
Defennder
Homework Helper
It takes a substitution to make things a lot easier as Hurkyl said.