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    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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    https://brainmass.com/math/calculus-and-analysis/eigenvalues-eigenfunctions-differential-equations-112806

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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, ...

    Solution Summary

    Eigenvalues, Eigenfunctions and Differential Equations are investigated.

    $2.49

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