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
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.