Problem:

and

bounded as

Find using separation of variables for general and write the solution in the form:

Eq. 1

Find in as explicit a form as you can, i.e., sum the series.

Attempt at solution:

After using the method of separation of variables I came to the solution:

Where

I'm just not sure how I'm supposed to combine these two pieces of information to be able to express in the form outlined in Eq. 1.

Any assistance would be greatly appreciated!