This paper concerns the stability analysis of first order delay differential equations with constant coefficients. As stability is a very important problem in the theory and application of ordinary as well as delay differential equations and moreover stability analysis of delay differential equations have been investigated extensively, although not completely developed for more complicated cases yet, here we first introduce the concept of stability region and stability boundaries of first order delay differential equation with constant coefficients. Finally we approximate the characteristics equation of first order linear delay differential equation with determinant of square matrices as constant coefficients, using inverse Laplace transform as well as Gamma function to determine the stability of the delay differential equations.
