Vol. 12, No. 1, 2019

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Antiderivatives and linear differential equations using matrices

Yotsanan Meemark and Songpon Sriwongsa

Vol. 12 (2019), No. 1, 151–156
Abstract

We show how to find the closed-form solutions for antiderivatives of xneax sinbx and xneax cosbx for all n 0 and a,b with a2 + b20 by using an idea of Rogers, who suggested using the inverse of the matrix for the differential operator. Additionally, we use the matrix to illustrate the method to find the particular solution for a nonhomogeneous linear differential equation with constant coefficients and forcing terms involving xneax sinbx or xneax cosbx.

Keywords
differential operator, inverse of matrix, rectangular form
Mathematical Subject Classification 2010
Primary: 15A09
Secondary: 34A30
Milestones
Received: 3 September 2017
Revised: 26 October 2017
Accepted: 14 December 2017
Published: 31 May 2018

Communicated by Kenneth S. Berenhaut
Authors
Yotsanan Meemark
Department of Mathematics and Computer Science
Faculty of Science
Chulalongkorn University
Bangkok
Thailand
Songpon Sriwongsa
Department of Mathematical Sciences
University of Wisconsin-Milwaukee
Milwaukee, WI
United States