HOMEWORK SET 5- LINEAR SYSTEMS (due 11/4)

Problems 1 to 6 below refer to a 2 X 2 system of the form

x'= Ax, x=x(t)=(x_1
(t), x_2 (t))

where the matrix A is found in the given problem in the
text.

For each system, *ignore the problem in the text except
for the matrix*

and do the following instead:

(i) find the general solution (real form);

(ii) sketch in the phase plane the trajectories with
ICs (1,0) and (0,1);

(iii) sketch the graphs of x_1 vs. t for the same ICs;

(iv) write down the fundamental matrix exp(tA)

Matrices A:

1. p. 541, no. 1

2. p. 541, no. 3

3. p. 541, no. 19

4. p. 541, no. 35

5. p. 549, no. 1

6. p.549, no. 5

The following three problems are from the text:

7. p.541, no. 46

8. p. 556, no. 12

9. p. 556, no. 14