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



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



[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.

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