The space-independent pile kinetic equations are solved to give the excess reactivity explicitly in terms of the rate of change of power and an integral over the past history of the power, the precursor densities being eliminated algebraically from the equations. The need for digital computations for determining the reactivity from a given power trace is thereby reduced. The solution is applicable to arbitrary variations of power with time and is examined in detail for the case of small damped oscillations, where it leads to simple algebraic expressions for the gain and phase angle. The behavior of the reactivity as a function of time is also computed for the case of a power fluctuation occurring during a short time interval, for a power trace which increases exponentially and then stays constant, and for a rapidly decaying power burst.