ANALYTIC SOLUTIONS OF A FUNCTIONAL DIFFERENTIAL EQUATION WITH STATE DEPENDENT ARGUMENT

Abstract

This paper is concerned with a functional differential equation $x'(z) = x(az + bx(z))$, where $a \neq 1$ and $b \neq 0$. By constructing a convergent power series solution $y(z)$ of a companion equation of the form $\beta y'(\beta z) = y'(z) [y (\beta ^2z) - ay(\beta z) + a]$, analytic solutions of the form $(y (\beta y^{-1} (z)) - az) /b$ for the original differential equation are obtained.