Solving a delay differential equation by two direct approaches

Abstract

: The Ambartsumian equation is an application of the theory of surface brightness in the milky way. It is a linear differential equation involving a proportional delay term. In this paper, two different approaches have been used to obtain the power series solution of Ambartsumian equation. The obtained series solution by the suggested approaches agrees with the published solution in the literature. However, the current approaches are not only very simple but also straightforward.