Solve:
$y_1'=12y_3$
$y_2'=y_1+13y3$
$y_3'=y_2$
(working from wolfram) http://www.wolframalpha.com/input/?i=%7B%7B0%2C0%2C12%7D%2C%7B1%2C0%2C13%7D%2C%7B0%2C1%2C0%7D%7D
so the solution is:
$y_1=3c_1e^{4x}-4c_2e^{-3x}-12c_3e^{-x}$
$y_2=4c_1e^{4x}-3c_2e^{-3x}-c_3e^{-x}$
$y_3=1c_1e^{4x}+c_2e^{-3x}+c_3e^{-x}$
now my question is: find a value y$(0)$ other than y$(0)$$=(0,0,0)$ such that y$(x)$ approaches $(0,0,0)$as $x$ approaches infinity.
Could someone explain what the question is asking?
Thanks! (note: I asked a similar question earlier, but this has corrected the error and changed the question)