Initial conditions for stability

[hbomb]

The general solution fo the following equations:

x'=2x-3y
y'=x-2y

Is, x=4C1e^2t, y=C1e^2t-3C2e^-2t

They ask for me to list a set of initial conditions (xo, yo) for which the solution is stable, i.e, (x, y)-->(0,0) for large t.

I don't understand this part of the problem.

 

[Office_Shredder]

Basically, for what constants C₁ and C₂ do x and y go to infinity as t gets large? From that, solve for what x(0) and y(0) can be

 

[hbomb]

Ok, I understand that for the general solution, the only unstable part of it is e^-2t. What does the setup of the solution look like?