Consider the boundary value problem y 2y + (1 + )y = 0, y(0) = 0, y(1) = 0. (a)
Chapter 11, Problem 17(choose chapter or problem)
Consider the boundary value problem y 2y + (1 + )y = 0, y(0) = 0, y(1) = 0. (a) Introduce a new dependent variable u by the relation y = s(x)u. Determine s(x) so that the differential equation for u has no u term. (b) Solve the boundary value problem for u and thereby determine the eigenvalues and eigenfunctions of the original problem. Assume that all eigenvalues are real. (c) Also solve the given problem directly (without introducing u).
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