Finding General Solution / Fundamental matrix

1. Dec 8, 2009

donkeystalk

Morning everyone,

Studying for a test and having a problem on a practice question he gave us to study with. Here's the question along with the answer:

Y' = AY + [e^t
e^-t
0]

with A =
[-1 0 4
-0 -1 2
0 0 1]

the answer given is: Y(t) =
[1/2(e^t - e^-t)
e^-t(t+1)
0]

My question is, what are the steps to getting to this solution, I've gone over notes, examples, scavenged the internet, not a whole lot of luck. I know it's probably out there, but I am probably looking up the wrong keywords via Google.

Any help with a general outline of what to do would be extremely helpful! Thanks a lot!

2. Dec 8, 2009

trambolin

You can search for the matrix exponential, and state equation in any linear systems book.

$$\dot x = Ax+Bu$$

is the form that you are looking for. The solution is a not-so-complicated convolution integral

3. Dec 8, 2009

donkeystalk

ok so what I am looking for is the state equation and matrix exponential?

this type of problem ended up not being on the exam,but I am guessing it will show up on the final in a just over a week.