# Diffusion equation, boundary conditions

1. Oct 1, 2011

### tomwilliam

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

1. The problem statement, all variables and given/known data

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

X(x) = Cekx+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.

2. Relevant equations

3. 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 Cekx + De-kx. As 1/x tends to 0 as x tends to infinity, can I assume that D/ekx also tends towards 0? Or does it tend to D? And what about C?

Thank in advance for any help

Last edited: Oct 1, 2011
2. Oct 1, 2011

### flyingpig

$$X(x) = Ce^{kx} + De^{-kx}$$

3. Oct 2, 2011

### 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