Solving system of nonlinear ODEs

Hello everyone,

I have a system on the form

$\displaystyle x''_1 + \lambda x'_1 + C(x_1)x_1 = A(x_1)x_3 + B(x_1)x_3^2 $

$\displaystyle x'_3 + D(x_1)x_3 + E(x_1)x'_1x_3 = F(x_1)x'_1 $

where $\displaystyle A,B,C,D,E,F$ are all nonlinear functions, and both $\displaystyle x_1, x_3$ depend on time.

Does anyone know a good book (if any) which covers methods for the solution of this type of system of nonlinear ODEs? Or will I have to use numerical integration?

Thanks

**Update:**

Indeed, I need an analytical solution to solve my original problem...