I present, apparently, a new description of radiative transfer problems in the time domain. It appears that for the first time a simple physical picture emerges of the underlying essence of scattered radiance when dealing with isotropic axially-symmetric scattering in nonconservative linear media as attenuated travelling waves was by analogy. The method used a new differential equation approach. Initially its accuracy in the frequency domain was demonstrated by applying it to a solved problem, where in the literature it is dealt with using the conventional 95-year-old integro-differential equation description. Confidence in the differential equation method was bolstered by showing how this new method produces the same analytical answer. The new technique converts the integro-differential equation formulation of radiative transfer into a “pure” differential equation formulation, consisting here in a mixture of ordinary and partial derivatives, and solves that. This paper analyzes the situation in the time domain using the differential equation description and again yields a travelling wave description. However, this time it is not simply by analogy that such a description is obtained. It is exact. This result of attenuated travelling waves was demonstrated in a prior paper by solving the integro-differential equation for the classic problem of axially-symmetric scalar isotropic scattering in a nonconservative linear medium. In this paper we revisit the problem, this time solving it by the differential equation method and obtain the identical result, once again confirming the method.