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**Rebesques** Ok... First of all, let $\displaystyle x_3=x_2$ and call the original equations (1), (2) respectively.

Now, (1) can be written as $\displaystyle x_1''+\lambda x_1'=W(x_1,x_2)$

where W is nonlinear in its arguments. By integrating, we obtain $\displaystyle x_1'=F_1(x_1,x_2)$, for a function $\displaystyle F_1$. Substitute this in (2), to end up with $\displaystyle x_2'=F_2(x_1,x_2)$, for a nonlinear function $\displaystyle F_2$.

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 $\displaystyle x_1=0,x_2=0$ (as I bet is the case) you can turn to a good book on asymptotic methods.