Originally Posted by

**rexhegemony** 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

y=[t+M/(k-kM)]/[t+1/(k-kM)]

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...