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