Consider the boundary-value problem y'' + y = 0, y(-) = y(), y'(-) = y'(). (a) The type of boundary conditions specified are called periodic

Consider the boundary-value problem

y'' + y = 0, y(-π) = y(π), y'(-π) = y'(π).

(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).