The differential operator Lis defined by d (e* 一 Ly = -e*y · - - dx dx (a) Determine the eigenvalues 1, of the problem, Ly, = \,eʻy, » 0 < x <1 dy 1 with boundary conditions y(0) = 0 +-y = 0 at x =1. dx 2 (b) Find the corresponding eigenfunctions, y,, and also a weight function p(x) with respect to which the y, are orthogonal.

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