Given the following Dif EQ's (linear):

Determine the values of , where is a constant, for which every solution has the property where as

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- Dec 9th 2007, 09:40 PMAuxiliaryChallenging Dif EQ
Given the following Dif EQ's (linear):

Determine the values of , where is a constant, for which every solution has the property where as - Dec 10th 2007, 05:14 AMTKHunny
Is there a determinant property that will solve this?

- Dec 10th 2007, 08:32 AMAuxiliary
- Dec 11th 2007, 04:01 PMAuxiliary
I plugged this in Maple, and found the eigenvalues and corresponding eigenvectors in terms of c.

The two eigenvalues are:

The corresponding eigenvectors, respectively, are:

[sqrt(c),1]

[-sqrt(c),1]

The multiplicities of both are 1. Not sure where to go with this...

When c = 0, we have repeated eigenvalues ...

When c is negative, we have complex numbers... I can't imagine complex numbers yielding X(t) -> 0 with t -> infinity ....

Ahh, very challenging.