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Your derivation seems OK to me. In particular, you get a system of differential equations equivalent to that listed in the Wikipedia page that you mention (modulo the change of notation A --> B, B --> A). The issue seems to be that Sage (actually Maxima) does not know how to solve this non-linear system, since you get the message:

ECL says: Error executing code in Maxima: desolve: can’t handle this case

Maybe you should try to simplify the system, as suggested in the Wikipedia page: adding the first two equations gives a simple equation: A B' - A' B = 0. Try then desolve with this equation and the third equation.