  We study the temporal equation of radiating stars by using three powerful
methods for the analysis of nonlinear differential equations. Specifically, we
investigate the global dynamics for the given master ordinary differential
equation to understand the evolution of solutions for various initial
conditions as also to investigate the existence of asymptotic solutions.
Moreover, with the application of Lie's theory, we can reduce the order of the
master differential equation, while an exact similarity solution is determined.
Finally, the master equation possesses the Painlev\'{e} property, which means
that the analytic solution can be expressed in terms of a Laurent expansion.
