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    Eigenvalue solutions of differential equations with boundary conditions.

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    Consider the equation: y'' + k*y = 0 with BC: y(0) = 0 , y() = a 0

    Answer the following:

    1. What are the restrictions on k such that there is a nontrivial solution?
    2. Find a solution using eigenfunction expansion on [0,]
    3. Find a solution to the differential equation using any method
    4. Compare answers 2 and 3 show they are equivalent

    Please see the attached file for the fully formatted problems.

    keywords: eigenvalues, eigenfunctions, ODEs

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    Solution Summary

    Eigenvalue solutions of differential equations with boundary conditions are investigated. The solution is detailed and well presented.