Thread: Challenging 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

Is there a determinant property that will solve this?

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.

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.