A class of exactly solvable reaction-diffusion equations with first-order distributed reaction rates

There has been considerable recent interest in reaction-diffusion equations in which the reaction kinetics are first order. These are suggested by a variety of applications exemplified by the theory of barrierless transitions. Because of the wide applicability of such systems a number of approximations have been suggested for their solution. We present here a new, exactly solvable equation of that form, which may be used to check these approximations.