Find the eigenvalues and eigenfunctions of the boundary-value problemx2y′′+xy′+ 9λy= 0, y′(1) = 0,y(e) = 0.   Put the equation in self-adjoint form, and give an orthogonality relation   Show that if ym and yn are two eigenfunctions corresponding to two different eigenvalues λm and λn respectively, then ym and yn are linearly independent

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A: The solution is given as

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A: Image is attached with detailed solution.

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