Problem Statement
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
My attempt a)
The first thing I do here (which may be where I'm going wrong) is that I rearrange the equation. I take
characteristic equation:
So
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