The reactor kinetic equations are reduced to an integral form convenient for explicit numerical solution, involving no approximations beyond the usual space-independent assumption. Numerical evaluation is performed by the RTS (Reactor Transient Solution) code, written in FORTRAN II for the IBM-704 computer. The characteristic roots and residues which arise in this method of solution have been computed and are tabulated in detail for each of the main fissile species. Analytic or point-function reactivity variation may be introduced, together with constant or time-varying reactivity compensation, and the resulting power response, total energy release, and compensated reactivity computed precisely as functions of time. The code solves the general non-equilibrium kinetics problem with extraneous sources, the customary equilibrium solution being a special case of the general solution. Practical use of the method is demonstrated through computed response curves for representative reactivity-addition functions in various types of chain-reacting systems.