I am trying to sketch the phase line and identify equilibrium and I am getting both solutions to be unstable , where I think the upper solution has to be stable and the lower one should be unstable

a) Sketch the phase line diagram for $\frac{dy}{dt} = (y-2)(y-5)^2$

b) Identify each equilibrium solutions as stable or unstable. Sketch the solutions corresponding to $y(0) = 3$

This is what I have: enter image description here

How would you do this?

  • $\begingroup$ If this is homework, please mark it as such. $\endgroup$ – Maroon Feb 23 '14 at 2:58
  • $\begingroup$ Could you tell what you have tried and done up to now ? $\endgroup$ – Claude Leibovici Feb 23 '14 at 4:46
  • $\begingroup$ Draw the directions on the lines $\endgroup$ – Hawk Feb 23 '14 at 5:00
  • $\begingroup$ @Amzoti did you just read that from my pic or you actually did the problem so you came to a conclusion ? $\endgroup$ – Bob Feb 24 '14 at 1:10
  • $\begingroup$ @Amzoti I got marked wrong by my professor...this was a question on my exam...no freaking way!!! $\endgroup$ – Bob Feb 24 '14 at 1:14

Here is a direction field for your problem.

It has many initial points included, plus direction. Notice that in one case, we have points leaving and in the other we approach from one side, but leave from the other.

enter image description here

enter image description here

  • $\begingroup$ thanks for taking the time to help me $\endgroup$ – Bob Feb 24 '14 at 1:45
  • $\begingroup$ even better, it shows the problem on there $\endgroup$ – Bob Feb 24 '14 at 1:57
  • $\begingroup$ Ahhh! My eyes have missed your phase portraits! $\endgroup$ – amWhy Feb 24 '14 at 13:34

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