Group methods for first oder neutral differential equation

Abstract

In this paper, we shall obtain a Lie type invariance condition for first order neutral differential equations using Taylor’s theorem for a function of several variables - an approach which is different from the existing literature for delay differential equations.A complete group classification of the first order linear neutral differential equation is made for which there is no literature. In addition, we have illustrated the group classification of a first order nonlinear neutral differential equation. Finally, as a special case we make a group classification of the first order delay differential equation.