A Generalized Method of Undetermined Coefficients

Authors

James S. Cook, Liberty UniversityFollow
William J. Cook, Appalachian State UniversityFollow

Publication Date

9-30-2022

Keywords

Undetermined coefficients, Annihilators, Cauchy-Euler

Disciplines

Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that are polynomial in a first order differential operator. In addition, we provide a number of constant coefficient, Cauchy-Euler, and novel examples.

Recommended Citation

Cook, James S. and Cook, William J. (2022) "A Generalized Method of Undetermined Coefficients," CODEE Journal: Vol. 15, Article 4.
Available at: https://scholarship.claremont.edu/codee/vol15/iss1/4