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  3. (a) find all positive values of ? for which the fo

(a) Find all positive values of ? for which the following boundary value problem has a...

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Advance Math

(a) Find all positive values of ? for which the followingboundary value problem has a nonzero solution. What are thecorresponding eigenfunctions? X?? + 4X? + (? + 4) X = 0, X?(0) = 0and X?(1) = 0. Hint: the roots of its auxiliary equation are –2 ±?i, where ? = ?2.

(b) Is ? = 0 an eigenvalue of this boundary value problem? Whyor why not?

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