Consider the eigenvalue problem with Robin BCs at both

Chapter 4, Problem 4.3.2

(choose chapter or problem)

Consider the eigenvalue problem with Robin BCs at both ends: X = X X(0)a0X(0)=0, X(l)+alX(l)=0. (a) Show that =0 is an eigenvalue if and only if a0 +al = a0all. (b) Findtheeigenfunctionscorrespondingtothezeroeigenvalue.(Hint: FirstsolvetheODEforX(x).Thesolutionsarenotsinesorcosines.)

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