We have investigated the spontaneous radiative decay of resonant nuclei in a planar x-ray waveguide after excitation by synchrotron radiation pulses. The waveguide acts as a cavity and modifies the mode structure of the electromagnetic field. As a result, the rate of spontaneous emission is enhanced by a factor proportional to the density of photon states in the cavity. In this experiment, we have observed a sixfold acceleration of the coherent radiative decay of 57Fe nuclei located in the center of the first-order guided mode. This is in very good agreement with theoretical predictions.