
Eigenfunction Expansion
Find the basic function at for
Also, find the solution which satisfies
What I don't understand is why the book multiplied through by x instead of of z = x + yi, because looking at the first solution, the imaginary constant is being used in relations to sqrt{4\lambda}.
How was acquired and is the coefficient 2 associated with sine in the first solutions due to solving for the conditions?
The solution to the problem is:

Then solve for the initial conditions?
What about taking into account if
When , the DE is reduced to , and then we have

Now, if , then we obtain:
So omega can't be 0; therefore, lambda can't equal 4.
Correct?

I don't understand how the book obtained its solution which would be for
When I do the problem, I obtain:
Before I attempt to solve , why am I so off with