So you have . We see that
and thus: For , the solution flows away from to minus infinity. For , the solution flows away from and tends to . And for , the solution flows away from to infinity.
If you have dx/dt = (x-2)(x-3)^2.
I know how to do the flow diagram and it has equilibrium points at x=2 (unstable) and x=3 (semi-stable?).
But am confused about this:
Describe the behaviour of x(t) as t -> infinity for different initial values x(0) = x0.
What do you do for this?