# Thread: Depict graphically the flow of the following equation...

1. ## Depict graphically the flow of the following equation...

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?).

2. So you have $x'=(x-2)(x-3)^2$. We see that
$x'\begin{cases}<0, \ x<2 \\ >0, \ x>2 \end{cases}$
and thus: For $x(0)=x_0<2$, the solution flows away from $x=2$ to minus infinity. For $x(0)=x_0\in(2,3)$, the solution flows away from $x=2$ and tends to $x=3$. And for $x(0)=x_0>3$, the solution flows away from $x=3$ to infinity.