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