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**1. Homework Statement**

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. Homework Equations**

y' = Ay

J = P[tex]^{-1}[/tex]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[tex]^{-1}[/tex]AP

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