ON THE EXACT SOLUTION OF THE FUNCTIONAL DIFFERENTIAL EQUATION y'(t) = ay(t) + by(-t)

Abdelhalim Ebaid; Hind K.Al-Jeaid

Abdelhalim Ebaid Department of Mathematics, Faculty of Science University of Tabuk, P.O.Box 741, Tabuk 71491, Kingdom of Saudi Arabia
Hind K.Al-Jeaid Department of Mathematical Sciences, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

Article ID: 2541

Keywords: functional differential equation; exact solution; series solution

Abstract

This paper focuses on obtaining the exact solution of the functional differential equation:y'(t)= ay(t)+ by(-t) subject to the initial condition y(0) =λ.The standard series approach is applied to obtain the solution in a power series form.The convergence issue is addressed.In addition, the exact solution is established in terms of elementary functions such as hyperbolic and trigonometric functions. The exact solutions of some special cases, at particular choices of a and b, are determined.The obtained results may be introduced for the first time regarding the solution of the current problem.

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