Show that is an eigenvalue of the Sturm- Liouville problem
and find a corresponding eigenfunction.
To start i posed that the solution of this problem will be in the form
using the end point conditions i get
this clearly gives us...
clearly If A=B=0 this would give us a dummy answer so i toss it, and say that first this equation to be true,
Where i am stuck is when i use the second endpoint condition i get...
with substitution + algebra putting the sin on one side and the cos on the other we get...
divide both sides by cos.....
substitute,
implies
SO how do i use this to prove is an eigenvalue, then how do i find my function.... please help