I sincerely wish somebody can help me to analytically solve following nonlinear ODE system. $x(t)$ $y(t)$ $z(t)$ are 3 functions of $t$, and I will ignore to write $t$ in the system. It's derived from multi-compartment model, with $x^2$ $y^2$ and $z^2$ more...
$\left\{ \begin{array}{l} x\prime=-x^2+x+y+z\\ y\prime=-y^2+x+y+z\\ z\prime=-z^2+x+y+z \end{array} \right.$
Furthermore, this system can be extended with with $n$ functions...
I do need close-forms of $x(t)$ $y(t)$ $z(t)$ so that I can do my later tasks... I will appreciate you a lot if you can offer me any solutions, hopefully a general solution for any $n$.
btw, I tried laplace transform, but after transmission, the system is still too hard to solve...
Thanks a lot! : )