  We study the behaviour of a radiating star when the interior expanding,
shearing fluid particles are traveling in geodesic motion. We demonstrate that
it is possible to obtain new classes of exact solutions in terms of elementary
functions without assuming a separable form for the gravitational potentials or
initially fixing the temporal evolution of the model unlike earlier treatments.
A systematic approach enables us to write the junction condition as a Riccati
equation which under particular conditions may be transformed into a separable
equation. New classes of solutions are generated which allow for mixed spatial
and temporal dependence in the metric functions. We regain particular models
found previously from our general classes of solutions.
