A formula substituting the undetermined coefficients and the annihilator methods

Abstract

This article presents an easy formula for obtaining a particular solution of a linear ordinary differential equation with constant real coefficients, , where f is a function given by a linear combination of polynomials, trigonometrical and exponential real function products. The desired solution is obtained through solving straightforward lower triangular linear systems with constant coefficients. Three examples are given.

Keywords:

• ordinary differential equations
• linear equations and systems
• linear differential equations
• complex exponential

AMS Subject Classifications::

• 34A30
• 97D40
• 30-01

Acknowledgements

I express my gratitude to Prof. Anthony W. Knapp for his suggestions and commentaries. I also thank Prof. L.A.F. Oliveira for his commentaries and to the referees for their time and very helpful remarks.