Differential Equations with Boundary Conditions : Eigenvalues, Eigenfunctions and Sturm-Liouville Problems

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

See attached file for full problem description.

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