Abstract: The reactor kinetics equations are combined into a single integral equation whose kernel describes the time-dependent characteristics of the reactor including six delayed groups of neutrons. Numerical solutions of the integral equation are given for constant, linear, and ∫sin²kx dx reactivities. An approximate solution of the integral equation is obtained which provides a basis for the formulation and solution of the reactor system control problem using the methods of servomechanisms theory. The reactor frequency response function, a product of the approximate solution, is calculated and plot given.