Differential Equations with Boundary Conditions : Eigenvalues, Eigenfunctions and Sturm-Liouville Problems
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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
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Eigenvalues, Eigenfunctions and Sturm-Liouville Problems are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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There is no way you can get the trivial solution for this equation. A trivial solution is y=0 for all x, but this can not be since already at the BC we state that y(pi)=a and a<>0.
However, there are certain values of k in which NO solution can be found. I indeed show that for all values of k other ...
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