**Problem 4: Eigenvalue Determination**Determine all negative eigenvalues for the differential equation:\[ \phi''(x) + 5\phi(x) = -\lambda \phi(x), \]with the boundary conditions:\[ \phi(0) = 0 \quad \text{and} \quad \phi(\pi) = 0. \]In this problem, you are tasked with finding the values of \(\lambda\) such that the given differential equation has solutions that satisfy the given boundary conditions.

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Answered: 4. Determine all negative eigenvalues…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Determine all negative eigenvalues for $" (x) + 5¢(x) = –Aø(x), with $(0) = 0 and ø(n) = 0. %3D