I just sincerely hope somebody can help me to analytically solve the following ODE system. $x(t)$, $y(t)$, $z(t)$ are $3$ functions of $t$, and $C_1, C_2, C_3, C_4, C_5, C_6$ are just constants.
$ \left\{ \begin{array}{l} x'(t)=[1-x(t)][C_1 y(t)+C_2 z(t)]\\ y'(t)=[1-y(t)][C_3 x(t)+C_4 z(t)]\\ z'(t)=[1-z(t)][C_5 x(t)+C_6 y(t)] \end{array} \right. $
I appreciate a lot if you can offer me any closed-form solutions analytically, especially a general solution with $N$ functions. Or if you can point me to any related materials, I will also appreciate. : )
Furthermore, if this is not solvable, is there any possible way to make approximation functions for them...?
Thanks a lot!