An Exposition on Solution Process and Nature of Solutions of Simple Delay Differential Equations

Abstract

This article gave an exposition on the solutions of single-delay autonomous linear differential equations with algorithmic presentations of the solution processes of two solution methods, with illustrative examples verifying the consistency of both solution methods. The article went further to examine the nature of solutions, obtaining in the process a complete characterization of all non-oscillatory solutions of a problem instance in the absence of initial functions. In the sequel the article proved that there is no nontrivial oscillatory solution if a constant initial function is specified for the delay differential equation in question and hence for delay differential equations in general.