Consider the eigenvalue problem
y″ + 2y′ + λy = 0; y(0) = y(1) = 0.
(a) Show that λ = 1 is not an eigenvalue. (b) Show that there is no eigenvalue λ such that λ < 1. (c) Show that the nth positive eigenvalue is λ = n2π2 + 1, with associated eigenfunction yn(x) = e−x sin nπx.
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