Plot the surface of the solutions to two or three parametric differential equations

I have a system of two differential equations in x(t) and y(t) which has no explicit solution. I can derive a numerical solution easily. I now have values for x(t) and y(t) for each moment in time, t. How do I plot the surface representation of the solutions x(t), y(t), t ?

[Stephan]

Dont you expect to get some kind of trajectory instead of a surface?