How to plot phase plane only using trajectory equation?

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.

Answer 1

[KSSV]

t = 0:0.01:10 ;  % define your time step 
C = 1 ;   % constant 
traj = C*exp(-6*t) ;
plot(t,traj)

[Byeongjae Kang]

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.......

Answer 2

[Les Beckham]

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'