I should state all linear subspaces for which the solutions for t->inf or t->-inf converge against x=0.
I think I have an idea what you mean. Let's take Now, we don't know the signs of and so we'll have to do different cases depending on which one we have. We may be able to do something clever with the signum function. I'll do the first component for to show you what's going on. We have
The trig functions are not going to either blow up or go to zero. Suppose Then the exponential blows up. Since we can't have that, the only option is if Otherwise, the component blows up. If, on the other hand, then it doesn't matter what and are, the component will go to zero.
Conversely, let's say we are looking at The situation will be precisely the opposite of the previous case. means a blow-up unless and means the component goes to zero regardless of what and are.
Does that help?
Hmm. Your solution is a space curve in 3 dimensions, with parameter t, right? Any of those CAS's should be able to plot that, although I'm not sure how to do that in Maple. I could probably figure it out in Mathematica. Captain Black is your best bet for MATLAB. I don't know who is especially good at Maple on this forum. I would definitely consult the help manual for information on parametric plotting.