Ok... First of all, let

and call the original equations (1), (2) respectively.

Now, (1) can be written as

where W is nonlinear in its arguments. By integrating, we obtain

, for a function

. Substitute this in (2), to end up with

, for a nonlinear function

.

So, the original system (1)+(2) is only an autonomous system of nonlinear first order ODEs. There is a rich theory behind autonomous systems, and you can get information about the qualitative behaviour of solutions in any good book on ODEs. Now, for obtaining solutions near

(as I bet is the case) you can turn to a good book on asymptotic methods.