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Homework Statement
I don't have a homework question. I have more of a general question.
Let's say we have a solution...
x=C1*[a1 a2][tex]^{T}[/tex]*e[tex]^{lamda1*t}[/tex] + C2*[b1 b2][tex]^{T}[/tex]*e[tex]^{lamda2*t}[/tex]
As t approaches infinity how do you determine what the solution does?
Homework Equations
The Attempt at a Solution
My guess is that a1,a2,b1,b2 don't matter.
If lamda1>0,lamda2>0 , and lamda1>lamda2 then as t approaches infinity then x will look more like the first term. As t approaches negative infinity the solution will look more like the second term.
If lamda1>0 and lamda2<0 then as t approaches infinity the solution will look more like first term. When t approaches negative infinity the solution will look more like the second term.
The coefficients (C1,C2) help determine whether the solution will approach negative infinity or infinity as t approaches one or the other.
So if the dominant term has a postive lamda and a negative coefficient then the solution will approach negative infinity as t approaches infinity?
So do I have it right?
Thank you for your time.