We have recently observed such sustained masers followed by long lasting tails extending over several tens of seconds in DNP-hyperpolarized samples. Following previous analyses of analogous experiments, the experiments were analyzed in classical terms using the nonlinear Bloch-Maxwell equations to take into account the coupling of the magnetization with the detection circuit. In this analysis, DNP was assumed to be in the thermal mixing regime, and described by the Provotorov equations. The combination of both phenomena results in the Bloch-Maxwell-Provotorov (BMP) equations that allow to shed some light onto the unusual nonlinear magnetization dynamics. However, the BMP esquations are deceptively simple, and are not amenable to an analytical analysis, except in particular cases where analytical solutions of the linearized BMP equations can be derived. Such a study nevertheless provides insight into the non intuitive behaviour of the magnetization dynamics.