Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to understand how to use phaseportraits in maple by following an example however, I'm not really sure where certian aspects of the equations given come from:

First, let us read in the package we will be using, and then enter the system above.

with(DEtools): with(plots):

> eq1:=diff(y1(t),t)=y1(t)+2*y2(t);

> eq2:=diff(y2(t),t)=2*y1(t)-y2(t);

Next we enter, as a list, some initial points. These points pick out which solutions we are on.


Finally, we ask Maple to do what it can with this system and these initial points!



Could someone explain where the initial points come from? e.g: 5 -5? I have no idea.



share|cite|improve this question
Initial conditions come from your original problem (e.g. the physical problem you're trying to solve). – user2468 Mar 6 '12 at 19:41
could you explain with regards to the above example? The initial problem is the two equations: eq1, eq2. I really don't understand where 5 and -5 have come from. – Euden Mar 6 '12 at 20:32
up vote 1 down vote accepted

Ideally you want to choose enough initial points to have at least one trajectory exhibiting each of the possible behaviours a trajectory of this system could have. So if there's a region of the plane that none of the existing ones enter, and you think something interesting might happen there, add another initial point in that region.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.