Question

Show that equilibrium point x_0=0 for the differential equation x'=0 is stable but not asymptotically stable.

Answer 1

The differential equation $$y'=0$$ Has the solution $$y=c$$ for any constant c,

Answer 2

that's right..

Answer 3

I don't know about your other stuff, a constant doesn't change with respect to anything, so I am not sure how its changing asymptotically

Answer 4

the proof relies on e-delta method

Answer 5

what chemistry :)

Answer 6

what is the "equilibrium point"

Answer 7

oh is that an ininital condition?

Answer 8

kinda

Answer 9

if $f(0)=0$, and $f(x)=c$, then the solution is $y=0$

Answer 10

I'm not sure this helps, but clearly this can't be an asymptotic equilibrium point since the derivative if the function itself is zero it can neither move towards or away from that point, hence it is not an asymptotic nor unstable equilibrium point

Answer 11

oh you have to use delta-epsilon? ugh, I'm out lol

Answer 12

(:

Answer 13

what do you mean by the delta epsilon?

Answer 14

method

Answer 15

I'll give the definition..

Answer 16

@Zarkon , @satellite73

Answer 17

@helder_edwin