Show that for the system x'' + 3x' + 2x = 0
x(0) = 0 x'(0) dosen't equal 0
it holds that x(t) dosen't equal 0 for all t.
I've got as far as y = Ae^-2x + Be^-x
and the differential of this.
Now im really stuck.
You've gotten as far as
Using the initial condition
If then either or . The latter only occurs at , as was already stated by the initial condition.
So the only other way that is if .
Recall that as stated originally.
This implies that .
Therefore, for any .