Show that the equilibrium point for the differential equation is stable but not asymptotically stable.

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- September 8th 2010, 10:51 AMjoestevensStable by but not Asymptotically Stable
Show that the equilibrium point for the differential equation is stable but not asymptotically stable.

- September 8th 2010, 06:29 PMJJMC89
- September 8th 2010, 06:30 PMjoestevens
- September 9th 2010, 05:26 AMJester
In this problem you can actually integrate and find the solution

Now, with gives your solution. Now perturb it so

.

So,

for all t (this a stable)

However, we don't have for some

(this a asymptotic stability).