# Homework Help: Fundamental set of solutions

1. Mar 19, 2008

### mbsl5

1. The problem statement, all variables and given/known data
Find a fundamental set of solutions to the system of differential equations:

y1' = 3*y1 - y2

y2' = y1 + y2

by reducing the problem to Jordan Canonical Form.

2. Relevant equations

y' = Ay
J = P$$^{-1}$$AP

3. The attempt at a solution
I have found the following:

(1) y' = Ay implies
A =
3 -1
1 1

(2) lamda (eigenvalue) = 2 with multiplicity 2

(3) So I believe
J (JCF) =
2 1
0 2

and P =
1 1
1 0

so that J = P$$^{-1}$$AP

Now I'm stuck. How do I use this to produce the fundamental set of solutions? Any help appreciated.