Question:

Consider the problem

with boundary conditions and

This problem is best solved by making the substitution and choosing so that satisfies a homogenous equation.

Find an explicit expression for and state the precise boundary conditions and equation which must satisfy. Do not find an explicit expression for

Attempted Answer:

Let

Choose

Then

and

so

so and therefore

and then

so

so

Can somebody please tell me if this is correct, and if not, could somebody please help me out?