I was solving a ODEs problem about semistable equilibrium solution.
The equation is dy/dt=k(1-y)^2. y(0) = M (M is an arbitrary constant)
It says the y=1 is a semistable solution for this equation, which other solutions below it approach it and those above it grow father away.
However when i get the general solution which is
i found that when t approaches infinity, the y correspondingly approaches 1 no matter the initial value M is either greater than 1 or smaller than 1.
If this is the case it seems that the qualitative analysis describing the characteristic of semistable solution is contradictory with what i got, i was
so confused about this.....
thank you very much for you valuable help,
thanks alot in advance...