Analytical and Numerical Simulations of a Delay Model: The Pantograph Delay Equation

In this paper, the pantograph delay differential equation y?(t)=ay(t)+byct subject to condition y(0)=? is reanalyzed for real constants a, b, and c. literature, it has been shown that equation, ?=1, well-posed if c<1, but not c>1. addition, solution available in form of a standard power series when ?=1. present research, we are able determine closed terms exponential functions. The convergence such analysed. It found converges c?(?1,1) ba<1 also c>1 a<0. For c=?1, exact obtained trigonometric functions, i.e., periodic with periodicity 2?b2?a2 b>a. current results introduced first time have reported relevant literature.