Problem

Consider the eigenvalue problemy″ + 2y′ + λy = 0; y(0) = 0, y′(1) = 0.Show that the eigenv...

Consider the eigenvalue problem

y″ + 2y′ + λy = 0; y(0) = 0, y′(1) = 0.

Show that the eigenvalues are all positive and that the nth positive eigenvalue is λn = α2n + 1 with associated eigenfunction yn(x) = e−x sin αnx, where α, is the nth positive root of tan z = z.

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Solutions For Problems in Chapter 2.8
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