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]