Hi, I need help on this problem
Sometimes a constant equilibrium solution has the property that solutions lying on one side of the equilibrium solution tend to approach it, whereas solutions lying on the other side depart from it. In this case the equilibrium solution is said to be semistable
Consider the equations
dy/dt = k(1 - y)^2 where k is a positive constant. Show that y=1 is the only critical point, with the corresponding equilibrium solution theta(t) = 1.
Thanks in advance