# Solving Non-Homogeneous Heat Equation

1. Oct 30, 2013

### temaire

1. The problem statement, all variables and given/known data
http://img546.imageshack.us/img546/4529/ztlg.png [Broken]

3. The attempt at a solution
I just want to know if I can use the following partial solution of another problem to get me to the point where I no longer have the $u$ term on the right side of the heat equation. The difference between my problem and the one below is that the boundary conditions are equal to zero, whereas one of mine isn't.

http://img819.imageshack.us/img819/803/x665.png [Broken]

Using the above partial solution, I was able to transform the original PDE to the following:

$w_{t} = w_{xx}$
$w(0,t) = 0, w(1,t) = e^{-t}$
$w(x.0) = 0$

where $u(x,t) = e^{-t}w(x,t)$

I would just like to know if the above transformation is correct before I go ahead with homogenizing the boundary conditions.

Last edited by a moderator: May 6, 2017