Group methods for second order delay differential equations

Abstract

In this research paper, we obtain the equivalent symmetries of non-homogeneous second order delay differential equations with variable coeffcients. Group methods have been used to do this. The approach followed by us to obtain a Lie type invariance condition for the second order delay differential equation is by using Taylor's theorem for a function of more than one variable. This Lie type invariance condition established by us in this paper, will be used to obtain the determining equations of the second order delay differential equation. We study certain cases under which the delay differential equation admits infinitesimal generators. Further, by performing symmetry analysis of this delay differential equation, the complete group classification for it has been made.