Eigenfunctions, Eigenvalues, Harmonic Functions and Sturm-Liouville Problems

Given the equation below find the eigenvalues and then the eigenfunctions. Compute the coefficients of the eigenfunction expansion. In each case determine what the eigenfunction expansion converges to on the interval and the sum of the first N terms on the same set of axes for the given interval.

Please show the function (N=5) and how it is expanded!!

f(x) = x^2 x is greater than or equal to -3 Pi or less than or equal to 3 Pi

y(-3Pi) = y(3Pi)..... y(-3Pi) = y(3Pi)

y'' + y = 0

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