Method of Undetermined Coefficients (aka: Method of Educated Guess)

Abstract

In this chapter, we will discuss one particularly simple-mi nded, yet often effective, method for finding particular solutions to nonhomogeneous differe ntial equations. As the above title suggests, the method is based on making “good guesses” regar din these particular solutions. And, as always, “good guessing” is usually aided by a thoroug h nderstanding of the problem (the ‘education’), and usually works best if the problem is s imple enough. Fortunately, you have had the necessary education, and a great many nonhomogeneou s differential equations of interest are sufficiently simple. As usual, we will start with second-order equations, and the n observe that everything developed also applies, with little modification, to similar nonh mogeneous differential equations of any order.