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1. Challenging Dif EQ

Given the following Dif EQ's (linear):

$\textbf{X}'=\left(\begin{array}{rr}-1 & c \\ 1 & -1 \end{array}\right)\textbf{X}$

Determine the values of $c$, where $c$ is a constant, for which every solution $\textbf{X}$ has the property where $\textbf{X}(t)\rightarrow \textbf{0}$ as $t\rightarrow \infty$

2. Is there a determinant property that will solve this?

3. Originally Posted by TKHunny
Is there a determinant property that will solve this?
I was thinking that maybe I have to do the Wronskian on this, but I'm not entirely sure.

4. I plugged this in Maple, and found the eigenvalues and corresponding eigenvectors in terms of c.

The two eigenvalues are:

$-1+\sqrt{c}$

$-1-\sqrt{c}$

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.

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