This Demonstration treats the homogeneous boundary case of the Sturm–Liouville eigenvalue problem by solving Airy's differential equation expanded around an ordinary point. The roots of this differential equation are called eigenvalues, and the corresponding functional solutions are known as eigenfunctions. Since solving for these eigenfunctions involves finding an infinite-dimensional matrix, algebra can be used to express solutions of the differential equation. After the eigenfunctions are generated, they are then plotted over a specified interval. The periodicity of these eigenfunctions stems from the fact that the boundary conditions used in this Demonstration were homogeneous.