# Given the differential equation: $\frac{dy}{dt} = (y-2)(y-5)^2$ sketch phase line and identify equilibrium

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:

How would you do this?

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