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How to plot phase plane only using trajectory equation?

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Byeongjae Kang
Byeongjae Kang on 10 May 2020
Edited: Les Beckham on 10 May 2020
In solving system of ODEs,
I got a general sol :
y1=c1*exp(-2t) + c2*exp(-4t)
y2=c1*exp(-2t) - c2*exp(-4t) (c1, c2 arbitrary constants)
By using this general sol,
I got a trajectory eq : y1^2 - y2^2 = C*exp(-6t) where C = 4*c1*c2.
How can I plot this equation ?
I already got a phase plane graph in textbook.
The most important point is I have to prove that the trajectory equation I got is correct equation of the phase plane.
please help me........
Thanks in advance.

Answers (2)

KSSV on 10 May 2020
t = 0:0.01:10 ; % define your time step
C = 1 ; % constant
traj = C*exp(-6*t) ;
  1 Comment
Byeongjae Kang
Byeongjae Kang on 10 May 2020
Thanks for your answer,
But your code is just t, traj plot.
I also have done this code
This does not mean phase plane.
phase plane should be plotted on y1y2-plane.
So I have to draw y1y2-plane with implicit parameter t.......

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Les Beckham
Les Beckham on 10 May 2020
Edited: Les Beckham on 10 May 2020
Try something like this:
c1 = 1; % replace with your desired constants
c2 = -1;
t=linspace(0, 10, 500); % adjust for your desired range of t
y1=c1*exp(-2*t) + c2*exp(-4*t);
y2=c1*exp(-2*t) - c2*exp(-4*t);
plot(y1, y2)
xlabel 'y1'
ylabel 'y2'

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