system of two non linear second order equations

Hi im having a problem for solving this set of equation and

i'm not that familiar with the ODE45 function in Matlab.

i would be glad if someone can help me with the following set of equations.

Thanks ,

Chen

[Zoltán Csáti]

Write the two second order ODEs as four first order one.

[chen]

ok . now i have four first order ODEs. they are dependent on each other. what should i do next?

[chen]

i have implemented the following for solving this system:

function xprime = Mirage(t,x);
k=2;
xprime=[x(1); k*(1-x(1).^2)./(1+k*x(2)); x(3) ; -(k*x(1)*x(3))./(1+k*x(2))];
end

x0=[1 1 1 1];
tspan=[0,20];
[t,x]=ode45(@Mirage,tspan,x0)

the program seems in infinite loop (Matlab stays"Busy"). where did i wrong?

[Torsten]

I get

xprime=[x(2); k*(1-x(2)^2)/(1+k*x(1)); x(4) ; -(k*x(2)*x(4))/(1+k*x(1))];

for your system where x(1)=y, x(2)=y', x(3)=z, x(4)=z'.

Best wishes

Torsten.