Boundary-value problem in differential equations

Question

Consider the problem:

$$u^{(4)} + \lambda u = 0, \ \ \ 0<x<\pi; \ \ \ u(0) = u(\pi) = u''(0) = u''(\pi) =0$$

Find the eigenvalues.

How should one proceed about this problem? I am complete lost in problems regarding boundary-value topics. Any help will be most appreciated.

Since the equation is linear you should determine general solutions deduced from the characteristic polynomial. From these solutions choose the ones that fulfill the boundary data. Have you tried this? — Quickbeam2k1, Mar 12 '13 at 07:39

score 1 · Accepted Answer · answered Mar 16 '13 at 21:33

1

Have you tried reading the relevant chapter in my book again? http://people.cs.uchicago.edu/~lebovitz/Eodesbook/bv.pdf

answered Mar 16 '13 at 21:33

Norman Lebovitz

1 Answers1