Predicting Long Term Behavior with Vector General Solution

[jimmy42]

Hello,

I have three differential equations, for these I have found the eigenvalues and eigenvectors. After that I made a vector general solution for the system of equations. From this vector, how can I predict the long term behaviour of the system?

-Thanks.

 

[HallsofIvy]

You know, I hope, that if $\lambda$ is an eigenvalue, then $e^{\lambda x}$ is a solution to the differnential equation. What happens to $e^{\lambda x}$ as x goes to infinity if the real part of $\lambda$ is negative?