Diff Eq: Initial Value Prob

1. Feb 8, 2005

BlkDaemon

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?

Thanks in advance.

BlackDaemon

2. Feb 9, 2005

Tide

You have a solution for the system. Generally, you will have a superpostion of two linearly independent solutions and you will adjust their coefficients to match the initial values.

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