Eigenvalues, Eigenfunctions and Differential Equations
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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 Differential Equations are investigated.
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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?
(1) k < 0. Let's write , where . Then the equation becomes and its general solution is . If we use the first boundary condition, y(0) = 0, we get . If we use the second condition y() = a, ...
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