The biggest challenge for me in attempting this problem is using the Linear algebra.

If I'm correct, I must:

1) Find eigenvalues.

2) Find eigenvectors.

3) Compute e^(At)

4) Multiply e^(At) by y_0 = y(0)

So, assuming what I said is correct, it seems like I know what I am doing but it's in setting up each step and then taking the result and moving to the next step that loses me so I would really appreciate if someone could show me how to set up each step and the answer each step gives to feed into the next step. I don't need mechanical computations (software outputs should most likely be fine).

Any help would be GREATLY appreciated!

Thanks in advance!