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Consider the Sturm-Liouville problem X′′(x) + λX(x) = 0 subject toX′(0) = 0, X(l) = 0. Are...

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Advance Math

Consider the Sturm-Liouville problem
X′′(x) + λX(x) = 0 subject toX′(0) = 0, X(l) = 0.

  1. Are the boundary conditions symmetric?

  2. Do these boundary conditions yield negative eigenvalues?
  3. Determine the eigenvalues and eigenfunctions, Xn(x). (It isenough in some cases to provide the equation that determines theeigenvalues rather than an explicit formula.)
  4. Are the eigenfunctions orthogonal?

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