Ok I (think I) see.

However, in your example, if b=0 then the a \neq 2 condition is not necessary, is it? In this maybe pathological case, the solution is trivially proportional to t^a. In this sense, the b-term has in my taste deeper implications than just being a perturbation.

Am I missing something trivial or am I putting too much emphasis on an irrelevant configuration?