Green's Functions for Ordinary Differential Equations

More than 50 years ago in a graduate course in differential equations, my colleagues and I struggled to understand what a Green's function for an ordinary differential equation really was. Suddenly, someone pointed to a green chalk mark on the blackboard and, with great glee, declared it to be the long-sought essence of the Green's function.
Years later, I could articulate that the Green's function was the kernel of an integral operator that inverted a differential operator. Only recently have I found that insight in literature other than my own. A search of the internet uncovered a chapter of a set of notes by Dr. Russell L. Herman (UNCW) in which he states "The inverse of a differential operator is an integral operator...The function is ... the kernel of the integral operator and is called the Green's function."
In this webinar, I'll show how the Green's function for a second-order ODE can be derived from the Variation of Parameters solution, and then I'll give examples of how Maple assists in finding Green's functions for different sets of boundary conditions: separated or mixed, homogeneous or nonhomogeneous.
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