You can not use $x(t+dt)= x(t)+vx(t)$ to calculate it.
$vx=\frac{dx}{dt}=limit_{\Delta t\rightarrow 0} \frac{x(t+\Delta t)-x(t)}{\Delta t}$

You can use $x(t+dt)= x(t)+vx(t)*dt$ for very small value, otherwise you will get a very large error.

You need to learn some numerical method to calculate it.
Please check out [url=http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods]Runge-Kutta 4th order method[/url]