Using chain rule to derive the path equation

[helpinghand]

r^' = 4r - rf
f^' = -3f + rf

In this question, there was three parts:
a) find all the critical points of this system.
b) Derive the linearised system about each critcal point...
c) Use the chain rule to derive the path equation of the trajectories in the phase plane.

I managed to get a and b out.

For c:

dr/df = dr/dt . dt/df

=> dr/df = (4r - rf)/(-3f - rf) ~~ not sure what to do from here.

I'm not sure how to get the path equation... Anyone have ideas?

Cheers

 

[tiny-tim]

hi helpinghand!

r^' = 4r - rf
f^' = -3f + rf
…
a) find all the critical points of this system.
b) Derive the linearised system about each critcal point...
c) Use the chain rule to derive the path equation of the trajectories in the phase plane.

hint: for (c), use (b)