Kinetic equations without the thermal feedback are integrated for an arbitrary reactivity variation, assuming that the magnitude of the changes in the excess reactivity is less than one dollar. First and second approximations are obtained. The results are applied to the step, ramp, and periodical reactivity changes. It is found that the logarithm of the flux, in the first approximation, is given by the function which is the solution of the linearized kinetic equations for the flux. Hence, the usual transfer function approach can be used to form the first approximate solution of the nonlinear kinetic equations. The wave form of the flux is obtained for a sinusoidal input, and the second harmonic is calculated. The exponential rise in the average value, as well as in the amplitude, of the oscillations of the flux is given for an alternative reactivity input. The gain of the reactor is defined. It is shown that the relative gain of the reactor decreases slightly with the increasing amplitude of the sinusoidal input. The results are compared to a numerical solution obtained by AVIDAC.