# Bounded Soloution of AN ODE

1. Dec 19, 2009

### TheForumLord

1. The problem statement, all variables and given/known data
Given this ode system:
x' = 2x+y-7e^(-t) -3
y'= -x+2y-1

Find all the bounded soloution in [a,infinity) when a is a real number...

I'm not realy sure what is a sufficient condition for bounded soloution in this question...Maybe there's something we can do and then we will not even need to solve the system...

Help is Needed!!

TNX a lot!

2. Relevant equations
3. The attempt at a solution
The eignvalues of the Matrix are: 2+-i...The eignvectors are: (1,i ) for 2+i & (1, -i ) for 2-i...
According to this we know that this is a fundemental set of soloutions for the homogenic system:
x1=e^2t[cost(1,0) -sint(0,1) ]
x2=e^2t[sint(1,0) +cost(0,1) ]
From here we can get to a private soloution of the whole system in several ways but they're all take very long time... I'm pretty sure there's an easier way to get to the bounded soloutions of the system...

HELP IS NEEDED ASAP!

TNX

2. Dec 19, 2009

### TheForumLord

NVM...I've managed to solve it on my own...
TNX anyway