I don\'t know how to do this problem. It has to be done in Maple. I need to code

Question

I don't know how to do this problem. It has to be done in Maple. I need to codes and instructions to do it..

d
--- x(t) = x (2 - x - y)
dt   
d
--- y(t) = y (y - x)
dt   
You may want to refer to the class notes for section 6.2.

1 - Use Maple ("solve") to find the equilibria. There should be three.

2 - Now use Maple ("dfieldplot") to draw the direction field. Make sure to choose x and y ranges that enclose all the equilibria - say at least one unit beyond all equilibria.

Which equilibria appear to be sources?

Which appear to be sinks?

Finally, pick one of the other two equilibria and linearize about it. Pick at least 4 initial conditions very near the origin and do the phaseportrait for the linearized system for a very brief time interval (so the curves do not "blow up"). Make sure that your initial conditions give you a representative set of solution curves surrounding the origin (i.e. curves in all four quadrants). One of these phaseportraits may look very unusual.

Explanation / Answer

for equilibrium conditions

dx/dt=0 and dy/dt=0

x(2-x-y)=0 and y(y-x)=0

By solving

x=0,y=0,y=x and x+y=2

(0,0),(1,1),(2,0)and (0,2)

0<=x<=2 and 0<=y<=2

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