ON THE EXACT SOLUTION OF THE FUNCTIONAL DIFFERENTIAL EQUATION $y^{\prime}(t)=a y(t)+b y(-t)$
Keywords:
functional differential equation, exact solution, series solution.DOI:
https://doi.org/10.17654/0974324322003Abstract
This paper focuses on obtaining the exact solution of the functional differential equation: $y^{\prime}(t)=a y(t)+b y(-t)$ subject to the initial condition $y(0)=\lambda $. 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.
Received: November 5, 2021
Accepted: December 2, 2021
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