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?