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 [itex]\lambda[/itex] is an eigenvalue, then [itex]e^{\lambda x}[/itex] is a solution to the differnential equation. What happens to [itex]e^{\lambda x}[/itex] as x goes to infinity if the real part of [itex]\lambda[/itex] is negative?