A system of DEs with variable coefficients.

[inertiagrav]

Hi. I have been trying for sometime to solve the following system of DEs analytically(Is it possible?) but no luck so far.
$$x''(t)=-z(t)x'(t)-x(t)+y(t),$$ $$y'(t)=-z(t)y(t)+x^2(t)$$ $$z'(t)=-2z^2(t)-x(t)$$.

With the initial conditions $x(0)=1$ , $x'(0)=0$ ,$y(0)=0$ and $z(0)=1$.

Thanks a lot in advance.

 

[Dr Transport]

nonlinear... start looking at a numerical solution

 

[BvU]

$z'(t)$ starts at -3 and things blow up after 1.6 seconds. What do these equations represent ? How long is it supposed to run ?

 

[inertiagrav]

Hello, thanks for your responses. I solved it numerically in Mathematica before posting it here, even for different sets of initial conditions. I am trying to get an approximate analytical solution and yea, i will ask for a context regarding the equations. Our Professor did say that if needed we can neglect the $x^2(t)$ term in $y'(t)$ but i still don't see how i can solve it.