Advanced Study on the Delay Differential Equation y?(t) = ay(t) + by(ct)

Many real-world problems have been modeled via delay differential equations. The pantograph equation y?(t)=ay(t)+byct belongs to such a set of To the authors’ knowledge, there are no standard methods solve equations, i.e., unlike ordinary for which numerous and well-known. In this paper, Adomian decomposition method is suggested analyze utilizing two different canonical forms. A power series solution obtained through first form, while second form leads exponential function solution. coincides with corresponding ones in literature special cases. Moreover, several exact solutions derived from present at specific restriction proportional parameter c terms parameters b. successfully closed then compared available (derived solution). results reveal that analysis efficient effective dealing