Consider a 3rd order linear homogeneous DE of the form
and for which and are solutions to the homogeneous form of (1).
Let . Give an example of a form of , and such that (1) has a stable equilibrium point and an example such that (1) has no stable equilibrium point.
When I think of stability, I immediately think of eigenvalues (nodes etc). Hence I reduced (1) into a system of linear equations:
This gives a corresponding matrix
But after working with this, I feel as if I'm not on the right track. Any advice would be greatly appreciated.