A Tree Combinatorial Structure on the Solution of a Delay Differential Equation: A Generating Function Approach.

This paper introduces a new approach for obtaining explicit solutions for a first order linear delay differential equation with constant coefficients. We conjecture that there is a generating function defined over of a specific class of polynomials in the delay that solves the equation, and prove in the main theorem that the conjecture is valid. We also show the advantage of our method as regards the traditional Method of Step Algorithm (MSA). [ABSTRACT FROM AUTHOR]