# Thread: System of first order ODE

1. I should state all linear subspaces for which the solutions for t->inf or t->-inf converge against x=0.

2. I think I have an idea what you mean. Let's take $t\to\infty.$ Now, we don't know the signs of $a$ and $b,$ 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 $t\to\infty,$ to show you what's going on. We have

$x(t)=e^{at}(c_{1}\sin(bt)+c_{2}\cos(bt)).$

The trig functions are not going to either blow up or go to zero. Suppose $a>0.$ Then the exponential blows up. Since we can't have that, the only option is if $c_{1}=c_{2}=0.$ Otherwise, the $x$ component blows up. If, on the other hand, $a<0,$ then it doesn't matter what $c_{1}$ and $c_{2}$ are, the $x$ component will go to zero.

Conversely, let's say we are looking at $t\to-\infty.$ The situation will be precisely the opposite of the previous case. $a<0$ means a blow-up unless $c_{1}=c_{2}=0,$ and $a>0$ means the component goes to zero regardless of what $c_{1}$ and $c_{2}$ are.

Does that help?

3. yes thank you very much, i thought of that already!

4. So you've got the final answer, then?

5. I was wondering how the plot of this system would look like (depending on (a,b) )? But I dont know how to plot it in maple?
Has anybody an idea?

thx

6. 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.

7. I know a bit about Maple. What exactly are you trying to plot?

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