**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