periodic boundary conditions

periodic boundary conditions

Consider the boundary-value problem
y” + ?y = 0, y(–p) = y(p), y'(–p) = y'( p).
(a) The type of boundary conditions specified are called periodic boundary conditions. Give a geometric interpretation of these conditions.
(b) Find the eigenvalues and eigenfunctions of the problem.

(c) Use a graphing utility to graph some of the eigenfunctions. Verify your geometric interpretation of the boundary conditions given in part (a).