Conditions for the most general bi-anisotropic medium in which any electromagnetic field can be decomposed into two uncoupled partial fields were recently introduced by one of the present authors. In the present paper it is shown that any electromagnetic source in this class of media can be decomposed into two sources creating uncoupled partial fields. Further, it is shown that for each of the problems the original bi-anisotropic medium can be replaced by a simpler equivalent medium for which an analytic Green dyadic can be found. This makes it possible to solve both decomposed problems in integral form.