Show that the eigenvalues and eigenfunctions of the boundaryvalue problem y ly 0, y(0)
Chapter 3, Problem 38(choose chapter or problem)
Show that the eigenvalues and eigenfunctions of the boundary-value problem
\(y^{\prime \prime}+\lambda y=0\), y(0)=0, \(y(1)+y^{\prime}(1)=0\)
are \(\lambda_{n}=\alpha_{n}^{2}\) and \(y_{n}=\sin \alpha_{n} x\), respectively, where \(\alpha_{n}\), \(n=1,2,3, \ldots\) are the consecutive positive roots of the equation \(\tan \alpha=-\alpha\).
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