# Maple: Understanding PhasePortraits

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.

inits:=[[y1(0)=5,y2(0)=-5],[y1(0)=-5,y2(0)=5]];

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

phaseportrait(feq1,eq2g,fy1(t),y2(t)g,t=-1..1,inits,

  view=[-10..10,-10..10],dirgrid=[50,50]);


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

Thanks,

Euden

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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

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.

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