  We propose a general method to analytically solve transport equations during
a cosmic phase transition without making approximations based on the assumption
that any transport coefficient is large. Using the MSSM as an example we derive
the solutions to a set of $3$ transport equations derived under the assumption
of supergauge equilibrium and the diffusion approximation. The result is then
rederived efficiently using a technique we present involving a parametrized
ansatz which turns the process of deriving a solution into an almost elementary
problem. We then show how both the derivation and the parametrized ansatz
technique can be generalized to solve an arbitrary number of transport
equations. Finally we derive a perturbative series that relaxes the usual
approximation that inactivates VEV dependent relaxation and CP violating source
terms at the bubble wall and through the symmetric phase.
