# Diff Eq: Initial Value Prob

I'm hacking at this particular linear system:

dY/dt = [1, -1; 1, 3] Y

I've already found myself a solution using the following function:

Y(t) = [ te^(2t), -(t+1)e^(2t) ]

That was fun, actually, once I figured out what the hell I was doing.

Here's my question: the next part of the problem asks for a solution to the intial value problem of the above differential equation, where

Y(0) = [0, 2]

I'm not sure how to attack the problem. Do I sub that matrix in for both values of Y, on both sides? If I do, then where do I put Y(t) so that this works out correctly? Or is there some other matrix multiplication step that I'm missing?

Any ideas?