Systems of ODEs (original) (raw)

I'm a graduate in chemical engineering taking a graduate ODE course. And, I'm having a little trouble with a couple homework problems. We're doing systems of first order ODEs which I've done previously in an undergrad ODE course a number of years ago, and slightly in a linear algebra course.

The first one I'm having trouble with is:

y' = [2 1; -1 1]y

I found the eigenvalues to be 1.5 +/- 0.866i
I don't deal with complex numbers very often, so I'm a little rusty. I know the two eigenvectors are complex conjugates, but I'm having a difficult time finding them. A little help?

The second one is x" + 3x' +2x = 0
The professor mentioned looking in the book to see how a higher order ODE can be converted to a series of first order ODEs, but the book only has like half a page on it, and I don't quite understand it.

Thanks.