PLEASE SEE ATTACHMENTS.
Solve question #3
Please see the attachment file.
Show that the equation can posses a non trivial solution which vanishes at and only if is such that , and that corresponding to such a characteristic number , any multiple of the function is a solution with the required properties.
We need to perform a function change in order to bring the equation to one of the known standard forms:
We try now a variable change of form
A non trivial solution is discussed.