I want to find the eigenvalues and the eigenfunctions of the operator
so we have the problem
Now I put in the functie y=A*exp(n*x), is it correct to do this?, and get the equation
but acording to the solutions it has to be Ln=n^2-k. Where do I make the mistake?
and how do I exactly determine the eigenfunctions
the boundary conditions are y(0)=0 and y(pi)=0
but how do I know what the the eigenfunction is? Here I can see it of course, but if I didn't know it for instance how do I start solving this problem?
The determining of the eigenvalue is not difficult after that.
thanks for the help
So you see it's not a question of finding the eigenfunction first and then the eigenvalue. They both emerge together as a result of solving the differential equation together with its boundary conditions.