Consider the problem y + y = 0, y(0) = 0, y (L) = 0. Show that if m and n are
Chapter 11, Problem 23(choose chapter or problem)
Consider the problem y + y = 0, y(0) = 0, y (L) = 0. Show that if m and n are eigenfunctions corresponding to the eigenvalues m and n, respectively, with m = n, then L 0 m(x)n(x) dx = 0. Hint: Note that m + mm = 0, n + nn = 0. Multiply the first of these equations by n, the second by m, and integrate from 0 to L, using integration by parts. Finally, subtract one equation from the other.
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