The absolute value of a solution

ChuckNoise

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Mar 5, 2019
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Hi

I got this example in my textbook, where i need a little help.


Dif.PNG

The problem i am having is only sort of related to the differential equation, nonetheless can anyone tell me why it follows that |x(t)| = e^-2t?

Thanks!
 
What does |x(t)| mean here? It is the magnitude of a vector, and if you expand that and apply the Pythagorean identity, you get e^{-2t}.
 
What does |x(t)| mean here? It is the magnitude of a vector, and if you expand that and apply the Pythagorean identity, you get e^{-2t}.
Of course! What a stupid mistake :D Thanks for pointing that out, in my mind i treated it like a scalar.

Thanks a lot
 
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