I am trying to identify the stable, unstable, and semistable critical points for the following differential equation: dydt=4y2(4−y2).
If I understand the definition of stable and unstable critical points, then it seems to me that the semi-stable point is at y=0 since in a neighborhood around y=0 we have the slope as positive. It also seems that y=−2,2 is a stable critical point since points around its neighborhood are negative for decreasing values and positive for increasing values. So it appears there are no unstable critical points. Am I on the right track here?
I also need to find k for y(t)→k given y(0)=1.4 and k for y(t)→k given y(0)=−3.2.
Any help anyone can provide is appreciated.
