# Analytic solutions of a functional differential equation with a state derivative dependent delay

Research paper by J.-G. Si, X.-P. Wang, S. S. Cheng

Indexed on: 01 Feb '99Published on: 01 Feb '99Published in: Aequationes mathematicae

#### Abstract

This paper is concerned with a functional differential equation of the form $$\alpha z+\beta x^{\prime}(z) = x(az+bx^{\prime }(z))$$ with the distinctive feature that the argument of the unknown function depends on the state derivative. Existence theorems are established for the analytic solutions and systematic methods for deriving explicit solutions are also given.