On Defining an Admitted Lie Group for First Order Delay Differential Equations with Constant Coefficients

Abstract

In this paper symmetry analysis is applied to first order delay differential equations with constant coefficients. The determining equations of the admitted Lie group are constructed. This procedure is similar to the way done for ordinary differential equations. The determining equations are then split with respect to the arbitrary elements, and then general solution can be found. The process of splitting the determining equation and solving it is also similar to that done for ordinary differential equations. We obtain the symmetry algebra admitted by this first order delay differential equation with constant coefficients.