1. \({\bf y}=c_{1}\left[\begin{array}{c}{1}\\[4pt]{1}\end{array}\right]e^{3t}+c_{2}\left[\begin{array}{c}{1}\\[4pt]{-1}\end{array}\right]e^{-t}\)
2. \({\bf y}=c_{1}\left[\begin{array}{c}{1}\\[4pt]{1}\end{array}\right]e^{-t/2}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{1}\end{array}\right]e^{-2t}\)
3. \({\bf y}=c_{1}\left[\begin{array}{c}{-3}\\[4pt]{1}\end{array}\right]e^{-t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{2}\end{array}\right]e^{-2t}\)
4. \({\bf y}=c_{1}\left[\begin{array}{c}{2}\\[4pt]{1}\end{array}\right]e^{-3t}+c_{2}\left[\begin{array}{c}{-2}\\[4pt]{1}\end{array}\right]e^{t}\)
5. \({\bf y}=c_{1}\left[\begin{array}{c}{1}\\[4pt]{1}\end{array}\right]e^{-2t}+c_{2}\left[\begin{array}{c}{-4}\\[4pt]{1}\end{array}\right]e^{3t}\)
6. \({\bf y}=c_{1}\left[\begin{array}{c}{3}\\[4pt]{2}\end{array}\right]e^{2t}+c_{2}\left[\begin{array}{c}{1}\\[4pt]{1}\end{array}\right]e^{t}\)
7. \({\bf y}=c_{1}\left[\begin{array}{c}{-3}\\[4pt]{1}\end{array}\right]e^{-5t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{1}\end{array}\right]e^{-3t}\)
8. \({\bf y}=c_{1}\left[\begin{array}{c}{1}\\[4pt]{2}\\[4pt]{1}\end{array}\right]e^{-3t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{-4}\\[4pt]{1}\end{array}\right]e^{-t}+c_{3}\left[\begin{array}{c}{-1}\\[4pt]{-1}\\[4pt]{1}\end{array}\right]e^{2t}\)
9. \({\bf y}=c_{1}\left[\begin{array}{c}{2}\\[4pt]{1}\\[4pt]{2}\end{array}\right]e^{-16t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{2}\\[4pt]{0}\end{array}\right]e^{2t}+c_{3}\left[\begin{array}{c}{-1}\\[4pt]{0}\\[4pt]{1}\end{array}\right]e^{2t}\)
10. \({\bf y}=c_{1}\left[\begin{array}{c}{-2}\\[4pt]{-4}\\[4pt]{3}\end{array}\right]e^{t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{1}\\[4pt]{0}\end{array}\right]e^{-2t}+c_{3}\left[\begin{array}{c}{-7}\\[4pt]{-5}\\[4pt]{4}\end{array}\right]e^{2t}\)
11. \({\bf y}=c_{1}\left[\begin{array}{c}{-1}\\[4pt]{-1}\\[4pt]{1}\end{array}\right]e^{-2t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{-2}\\[4pt]{1}\end{array}\right]e^{-3t}+c_{3}\left[\begin{array}{c}{-2}\\[4pt]{-6}\\[4pt]{3}\end{array}\right]e^{-5t}\)
12. \({\bf y}=c_{1}\left[\begin{array}{c}{11}\\[4pt]{7}\\[4pt]{1}\end{array}\right]e^{3t}+c_{2}\left[\begin{array}{c}{1}\\[4pt]{2}\\[4pt]{1}\end{array}\right]e^{-2t}+c_{3}\left[\begin{array}{c}{1}\\[4pt]{1}\\[4pt]{1}\end{array}\right]e^{-t}\)
13. \({\bf y}=c_{1}\left[\begin{array}{c}{4}\\[4pt]{-1}\\[4pt]{1}\end{array}\right]e^{-4t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{-1}\\[4pt]{1}\end{array}\right]e^{6t}+c_{3}\left[\begin{array}{c}{-1}\\[4pt]{0}\\[4pt]{1}\end{array}\right]e^{4t}\)
14. \({\bf y}=c_{1}\left[\begin{array}{c}{1}\\[4pt]{1}\\[4pt]{5}\end{array}\right]e^{-5t}+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{0}\\[4pt]{1}\end{array}\right]e^{5t}+c_{3}\left[\begin{array}{c}{1}\\[4pt]{1}\\[4pt]{0}\end{array}\right]e^{5t}\)
15. \({\bf y}=c_{1}\left[\begin{array}{c}{1}\\[4pt]{-1}\\[4pt]{2}\end{array}\right]+c_{2}\left[\begin{array}{c}{-1}\\[4pt]{0}\\[4pt]{3}\end{array}\right]e^{6t}+c_{3}\left[\begin{array}{c}{1}\\[4pt]{3}\\[4pt]{0}\end{array}\right]e^{6t}\)
16. \({\bf y}=-\left[\begin{array}{c}{2}\\[4pt]{6}\end{array}\right]e^{5t}+\left[\begin{array}{c}{4}\\[4pt]{2}\end{array}\right]e^{-5t}\)
17. \({\bf y}=\left[\begin{array}{c}{2}\\[4pt]{-4}\end{array}\right]e^{t/2}+\left[\begin{array}{c}{-2}\\[4pt]{1}\end{array}\right]e^{t}\)
18. \({\bf y}=\left[\begin{array}{c}{7}\\[4pt]{7}\end{array}\right]e^{9t}-\left[\begin{array}{c}{2}\\[4pt]{4}\end{array}\right]e^{-3t}\)
19. \({\bf y}=\left[\begin{array}{c}{3}\\[4pt]{9}\end{array}\right]e^{5t}-\left[\begin{array}{c}{4}\\[4pt]{2}\end{array}\right]e^{-5t}\)
20. \({\bf y}=\left[\begin{array}{c}{5}\\[4pt]{5}\\[4pt]{0}\end{array}\right]e^{t/2}+\left[\begin{array}{c}{0}\\[4pt]{0}\\[4pt]{1}\end{array}\right]e^{t/2}+\left[\begin{array}{c}{-1}\\[4pt]{2}\\[4pt]{0}\end{array}\right]e^{-t/2}\)
21. \({\bf y}=\left[\begin{array}{c}{3}\\[4pt]{3}\\[4pt]{3}\end{array}\right]e^{t}+\left[\begin{array}{c}{-2}\\[4pt]{-2}\\[4pt]{2}\end{array}\right]e^{-t}\)
22. \({\bf y}=\left[\begin{array}{c}{2}\\[4pt]{-2}\\[4pt]{2}\end{array}\right]e^{t}-\left[\begin{array}{c}{3}\\[4pt]{0}\\[4pt]{3}\end{array}\right]e^{-2t}+\left[\begin{array}{c}{1}\\[4pt]{1}\\[4pt]{0}\end{array}\right]e^{3t}\)
23. \({\bf y}=-\left[\begin{array}{c}{1}\\[4pt]{2}\\[4pt]{1}\end{array}\right]e^{t}+\left[\begin{array}{c}{4}\\[4pt]{2}\\[4pt]{4}\end{array}\right]e^{-t}+\left[\begin{array}{c}{1}\\[4pt]{1}\\[4pt]{0}\end{array}\right]e^{2t}\)
24. \({\bf y}=\left[\begin{array}{c}{-2}\\[4pt]{-2}\\[4pt]{2}\end{array}\right]e^{2t}-\left[\begin{array}{c}{0}\\[4pt]{3}\\[4pt]{0}\end{array}\right]e^{-2t}+\left[\begin{array}{c}{4}\\[4pt]{12}\\[4pt]{4}\end{array}\right]e^{4t}\)
25. \({\bf y}=\left[\begin{array}{c}{-1}\\[4pt]{-1}\\[4pt]{1}\end{array}\right]e^{-6t}+\left[\begin{array}{c}{2}\\[4pt]{-2}\\[4pt]{2}\end{array}\right]e^{2t}+\left[\begin{array}{c}{7}\\[4pt]{-7}\\[4pt]{-7}\end{array}\right]e^{4t}\)
26. \({\bf y}=\left[\begin{array}{c}{1}\\[4pt]{4}\\[4pt]{4}\end{array}\right]e^{-t}+\left[\begin{array}{c}{6}\\[4pt]{6}\\[4pt]{-2}\end{array}\right]e^{2t}\)
27. \({\bf y}=\left[\begin{array}{c}{4}\\[4pt]{-2}\\[4pt]{2}\end{array}\right]+\left[\begin{array}{c}{3}\\[4pt]{-9}\\[4pt]{6}\end{array}\right]e^{4t}+\left[\begin{array}{c}{-1}\\[4pt]{1}\\[4pt]{-1}\end{array}\right]e^{2t}\)
29. Half lines of \(L_{1} : y_{2} = y_{1}\) and \(L_{2} : y_{2} = −y_{1}\) are trajectories other trajectories are asymptotically tangent to \(L_{1}\) as \(t → −∞\) and asymptotically tangent to \(L_{2}\) as \(t → ∞\).
30. Half lines of \(L_{1} : y_{2} = −2y_{1}\) and \(L_{2} : y_{2} = −y_{1}/3\) are trajectories other trajectories are asymptotically parallel to \(L_{1}\) as \(t → −∞\) and asymptotically tangent to \(L_{2}\) as \(t → ∞\).
31. Half lines of \(L_{1} : y_{2} = y_{1}/3\) and \(L_{2} : y_{2} = −y_{1}\) are trajectories other trajectories are asymptotically tangent to \(L_{1}\) as \(t → −∞\) and asymptotically parallel to \(L_{2}\) as \(t → ∞\).
32. Half lines of \(L_{1} : y_{2} = y_{1}/2\) and \(L_{2} : y_{2} = −y_{1}\) are trajectories other trajectories are asymptotically tangent to \(L_{1}\) as \(t → −∞\) and asymptotically tangent to \(L_{2}\) as \(t → ∞\).
33. Half lines of \(L_{1} : y_{2} = −y_{1}/4\) and \(L_{2} : y_{2} = −y_{1}\) are trajectories other trajectories are asymptotically tangent to \(L_{1}\) as \(t → −∞\) and asymptotically parallel to \(L_{2}\) as \(t → ∞\).
34. Half lines of \(L_{1} : y_{2} = −y_{1}\) and \(L_{2} : y_{2} = 3y_{1}\) are trajectories other trajectories are asymptotically parallel to \(L_{1}\) as \(t → −∞\) and asymptotically tangent to \(L_{2}\) as \(t → ∞\).
36. Points on \(L_{2} : y_{2} = y_{1}\) are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of \(L_{1}\), parallel to \(\left[\begin{array}{c}{1}\\[4pt]{-1}\end{array}\right]\), traversed toward L1.
37. Points on \(L_{1} : y_{2} = −y_{1}/3\) are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of \(L_{1}\), parallel to \(\left[\begin{array}{c}{-1}\\[4pt]{2}\end{array}\right]\), traversed away from \(L_{1}\).
38. Points on \(L_{1} : y_{2} = y_{1}/3\) are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of \(L_{1}\), parallel to \(\left[\begin{array}{c}{1}\\[4pt]{-1}\end{array}\right]\),\(\left[\begin{array}{c}{-1}\\[4pt]{1}\end{array}\right]\), traversed away from \(L_{1}\).
39. Points on \(L_{1} : y_{2} = y_{1}/2\) are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of \(L_{1}\), parallel to \(\left[\begin{array}{c}{1}\\[4pt]{-1}\end{array}\right]\), \(L_{1}\).
40. Points on \(L_{2} : y_{2} = −y_{1}\) are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of \(L_{2}\), parallel to \(\left[\begin{array}{c}{-4}\\[4pt]{1}\end{array}\right]\), traversed toward \(L_{1}\).
41. Points on \(L_{1} : y_{2} = 3y_{1}\) are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of \(L_{1}\), parallel to \(\left[\begin{array}{c}{1}\\[4pt]{-1}\end{array}\right]\), traversed away from \(L_{1}\).
