Diffusion equation, boundary conditions

[tomwilliam]

EDIT: The subscripts in this question should all be superscripts!

Homework Statement

I'm trying to solve a temperature problem involving the diffusion equation, which has led me to the expression:

X(x) = Ce_kx+De_-kx

Where U(x,y) = X(x)Y(y)
and I am ignoring any expressions where Y(y)=0 or X(x)=0 for all values of their variables as these are trivial solutions.

I'm told I can simplify things by applying one of the boundary conditions:

As x tends towards infinity, U(x,y) tends towards 0.

Homework Equations

The Attempt at a Solution

So my question is, how do I apply this to the general solution I've found for X(x)?
I know that Y(y) is not zero, so I effectively have X(x) going to zero as x tends towards infinity. So I need to work out what happens to Ce_kx + De_-kx. As 1/x tends to 0 as x tends to infinity, can I assume that D/e_kx also tends towards 0? Or does it tend to D? And what about C?

Thank in advance for any help

 

[flyingpig]

Is this your equation...?

[tex]X(x) = Ce^{kx} + De^{-kx}[/tex]

 

[tomwilliam]

Yes, that's right.

I've worked out that C=0 as this is the only way to ensure X(x)=0 as x tends to infinity.

Thanks anyway