  Time-dependent Lindblad master equations have important applications in areas
ranging from quantum thermodynamics to dissipative quantum computing. In this
paper we outline a general method for writing down exact solutions of
time-dependent Lindblad equations whose superoperators form closed algebras. We
focus on the particular case of a single qubit and study the exact solution
generated by both coherent and incoherent mechanisms. We also show that if the
time-dependence is periodic, the problem may be recast in terms of Floquet
theory. As an application, we give an exact solution for a two-levels quantum
heat engine operating in a finite-time.
