# A A system of DEs with variable coefficients.

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1. Jun 9, 2017

### 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 $z(0)=1$.

2. Jun 9, 2017

### Dr Transport

nonlinear.... start looking at a numerical solution

3. Jun 9, 2017

### 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 ?

4. Jun 10, 2017

### 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.