12. Consider the eigenvalue problem y" + ìy = 0; y(-n)= y(1), y'(-x) = y'(1), which is not of the type in (10) because the two endpoint conditions are not "separated" between the two endpoints. (a) Show that 2o = 0 is an eigenvalue with associated eigenfunction yo(x) = 1. (b) Show that there are no neg- ative eigenvalues. (c) Show that the nth positive eigen- value is n2 and that it has two linearly independent associ- ated eigenfunctions, cos nx and sin nx.

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