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.