#### Vol. 12, No. 1, 2019

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
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 ${x}^{n}{e}^{ax}sinbx$ and ${x}^{n}{e}^{ax}cosbx$ for all $n\in {ℕ}_{0}$ and $a,b\in ℝ$ with ${a}^{2}+{b}^{2}\ne 0$ 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 ${x}^{n}{e}^{ax}sinbx$ or ${x}^{n}{e}^{ax}cosbx$.

We have not been able to recognize your IP address 3.239.119.61 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

##### Keywords
differential operator, inverse of matrix, rectangular form
Primary: 15A09
Secondary: 34A30