Analytic Solutions of a Second-Order Functional Differential Equation

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Abstract

In this paper we examine the nature of the secondary order differential equation analytical solutions with a state derivative formal delay Considering a convergent power series g(z) of a secondary equation + with the relation p(z) + , we obtain an analytic solution x(z). Furthermore, we characterize a polynomial solution when p(z) is a polynomial. We built a corresponding auxiliary equation with parameter to obtain analytical solutions of the problem. . The existence of solutions of an auxillary equation depends on the condition of a parameter , such as is in the unit circle and is a root of unity which satisfies the Diophantine condition.