I would like to study the following system non-linear ode system because I hope to gain some insight into the curvature of a related metric. \begin{align} (q'_1 + q'_2) &= \frac{2}{3}\big(A_1e^{-q_1} + Ce^{-(2q_1 + q_2)}\big) \\ q_2'(q_1' + q_2') &= 4\big(A_2e^{q_2} - Ce^{-(2q_1 + q_2)}\big) \end{align} where the $A_i$ and $C$ are constants and the functions $q_i = q_i(t)$ are real valued functions of one real variable.
Now I am a complete beginner when it comes to non-linear ode unfortunately and the literature on this topic is huge, hence I was wondering whether some expert eye may spot certain characteristics in these equations (e.g. whether they fall into a particular class of equations for which some technique is particularly useful) and point me to more targeted references? I would be totally happy about a recommendation like a chapter in one of the classics so that I know what I have to focus on.
Many thanks for the help!!