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.

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- Apr 15th 2009, 07:06 AM #1

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- Apr 15th 2009, 07:18 AM #2
OK, first off, clearly x(t) DOES equal 0 at a value of t, namely t = 0. So I assume you meant that it holds that x(t) doesn't equal 0 for all OTHER t.

You've gotten as far as

.

Using the initial condition

.

So

.

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.

So .

This implies that .

Therefore, for any .

- Apr 15th 2009, 07:27 AM #3

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- Apr 15th 2009, 07:32 AM #4