The temperature, , of a cooling fin of a finite length, , satisfies
where , , and are constants
a) Find the complimentary function , stating your answer in terms of unknown constants, and
b)Complete the following identity
c) write down your starting point for the particular solution,
d) find and the coefficients , and and hence show that hte solution of the above problem is
The first thing I do here (which may be where I'm going wrong) is that I rearrange the equation. I take
With this, I jump straight to
I can then verify that is a solution, with . But this helps me very little when I try to solve for my initial values and helps me less when I try to complete part (d).
Grinding through a bit further I can solve for with initial values with
So my new
But then attempting to solve for I get stuck. I end up with
And I think I'm stuck.
Am I missing some simple algebra trick here, or have I gone down the wrong road?
I'm pretty sure that's right, at least.
So, I'm thinking I'm starting this wrong, but I can't think of another way to attempt this. Any help would be greatly appreciated.