# A Sturm-Liouville Eigenvalue Problem

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This Demonstration shows solutions to the Sturm–Liouville eigenvalue problem subject to the boundary conditions and .

Contributed by: Tania Mata (December 2020)

Suggested by: Rafael Fernandez

With additional contributions by: Tomas Garza and Rafael Fernandez

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This equation may be written as a Cauchy–Euler equation , where .

Solutions are of the form

.

You can vary the parameters and .

The eigenvalues are

.

References

[1] M. Al-Gwaiz, *Sturm–Liouville Theory and Its Applications*, London: Springer, January 2008.

[2] A. Zettl, *Sturm–Liouville Theory*, Providence, RI: American Mathematical Society, 2005.

[3] M. L. Abell and J. P. Braselton, *Differential Equations with Mathematica*, 3rd ed., Boston: Elsevier, 2004.

[4] R. L. Herman, *A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems*,* *Monograph, December 2008. (Oct 1, 2020) people.uncw.edu/hermanr/mat463/ODEBook/Book/ODE_Main.pdf.

## Permanent Citation