

1. $${\bf y}=c_{1}\left[\begin{array}{c}{1}\\{1}\end{array}\right]e^{3t}+c_{2}\left[\begin{array}{c}{1}\\{-1}\end{array}\right]e^{-t}$$

2. $${\bf y}=c_{1}\left[\begin{array}{c}{1}\\{1}\end{array}\right]e^{-t/2}+c_{2}\left[\begin{array}{c}{-1}\\{1}\end{array}\right]e^{-2t}$$

3. $${\bf y}=c_{1}\left[\begin{array}{c}{-3}\\{1}\end{array}\right]e^{-t}+c_{2}\left[\begin{array}{c}{-1}\\{2}\end{array}\right]e^{-2t}$$

4. $${\bf y}=c_{1}\left[\begin{array}{c}{2}\\{1}\end{array}\right]e^{-3t}+c_{2}\left[\begin{array}{c}{-2}\\{1}\end{array}\right]e^{t}$$

5. $${\bf y}=c_{1}\left[\begin{array}{c}{1}\\{1}\end{array}\right]e^{-2t}+c_{2}\left[\begin{array}{c}{-4}\\{1}\end{array}\right]e^{3t}$$

6. $${\bf y}=c_{1}\left[\begin{array}{c}{3}\\{2}\end{array}\right]e^{2t}+c_{2}\left[\begin{array}{c}{1}\\{1}\end{array}\right]e^{t}$$

7.  $${\bf y}=c_{1}\left[\begin{array}{c}{-3}\\{1}\end{array}\right]e^{-5t}+c_{2}\left[\begin{array}{c}{-1}\\{1}\end{array}\right]e^{-3t}$$

8.  $${\bf y}=c_{1}\left[\begin{array}{c}{1}\\{2}\\{1}\end{array}\right]e^{-3t}+c_{2}\left[\begin{array}{c}{-1}\\{-4}\\{1}\end{array}\right]e^{-t}+c_{3}\left[\begin{array}{c}{-1}\\{-1}\\{1}\end{array}\right]e^{2t}$$

9.  $${\bf y}=c_{1}\left[\begin{array}{c}{2}\\{1}\\{2}\end{array}\right]e^{-16t}+c_{2}\left[\begin{array}{c}{-1}\\{2}\\{0}\end{array}\right]e^{2t}+c_{3}\left[\begin{array}{c}{-1}\\{0}\\{1}\end{array}\right]e^{2t}$$

10.  $${\bf y}=c_{1}\left[\begin{array}{c}{-2}\\{-4}\\{3}\end{array}\right]e^{t}+c_{2}\left[\begin{array}{c}{-1}\\{1}\\{0}\end{array}\right]e^{-2t}+c_{3}\left[\begin{array}{c}{-7}\\{-5}\\{4}\end{array}\right]e^{2t}$$

11.  $${\bf y}=c_{1}\left[\begin{array}{c}{-1}\\{-1}\\{1}\end{array}\right]e^{-2t}+c_{2}\left[\begin{array}{c}{-1}\\{-2}\\{1}\end{array}\right]e^{-3t}+c_{3}\left[\begin{array}{c}{-2}\\{-6}\\{3}\end{array}\right]e^{-5t}$$

12.  $${\bf y}=c_{1}\left[\begin{array}{c}{11}\\{7}\\{1}\end{array}\right]e^{3t}+c_{2}\left[\begin{array}{c}{1}\\{2}\\{1}\end{array}\right]e^{-2t}+c_{3}\left[\begin{array}{c}{1}\\{1}\\{1}\end{array}\right]e^{-t}$$

13.  $${\bf y}=c_{1}\left[\begin{array}{c}{4}\\{-1}\\{1}\end{array}\right]e^{-4t}+c_{2}\left[\begin{array}{c}{-1}\\{-1}\\{1}\end{array}\right]e^{6t}+c_{3}\left[\begin{array}{c}{-1}\\{0}\\{1}\end{array}\right]e^{4t}$$

14.  $${\bf y}=c_{1}\left[\begin{array}{c}{1}\\{1}\\{5}\end{array}\right]e^{-5t}+c_{2}\left[\begin{array}{c}{-1}\\{0}\\{1}\end{array}\right]e^{5t}+c_{3}\left[\begin{array}{c}{1}\\{1}\\{0}\end{array}\right]e^{5t}$$

15.  $${\bf y}=c_{1}\left[\begin{array}{c}{1}\\{-1}\\{2}\end{array}\right]+c_{2}\left[\begin{array}{c}{-1}\\{0}\\{3}\end{array}\right]e^{6t}+c_{3}\left[\begin{array}{c}{1}\\{3}\\{0}\end{array}\right]e^{6t}$$

16. $${\bf y}=-\left[\begin{array}{c}{2}\\{6}\end{array}\right]e^{5t}+\left[\begin{array}{c}{4}\\{2}\end{array}\right]e^{-5t}$$

17. $${\bf y}=\left[\begin{array}{c}{2}\\{-4}\end{array}\right]e^{t/2}+\left[\begin{array}{c}{-2}\\{1}\end{array}\right]e^{t}$$

18. $${\bf y}=\left[\begin{array}{c}{7}\\{7}\end{array}\right]e^{9t}-\left[\begin{array}{c}{2}\\{4}\end{array}\right]e^{-3t}$$

19. $${\bf y}=\left[\begin{array}{c}{3}\\{9}\end{array}\right]e^{5t}-\left[\begin{array}{c}{4}\\{2}\end{array}\right]e^{-5t}$$

20. $${\bf y}=\left[\begin{array}{c}{5}\\{5}\\{0}\end{array}\right]e^{t/2}+\left[\begin{array}{c}{0}\\{0}\\{1}\end{array}\right]e^{t/2}+\left[\begin{array}{c}{-1}\\{2}\\{0}\end{array}\right]e^{-t/2}$$

21. $${\bf y}=\left[\begin{array}{c}{3}\\{3}\\{3}\end{array}\right]e^{t}+\left[\begin{array}{c}{-2}\\{-2}\\{2}\end{array}\right]e^{-t}$$

22. $${\bf y}=\left[\begin{array}{c}{2}\\{-2}\\{2}\end{array}\right]e^{t}-\left[\begin{array}{c}{3}\\{0}\\{3}\end{array}\right]e^{-2t}+\left[\begin{array}{c}{1}\\{1}\\{0}\end{array}\right]e^{3t}$$

23. $${\bf y}=-\left[\begin{array}{c}{1}\\{2}\\{1}\end{array}\right]e^{t}+\left[\begin{array}{c}{4}\\{2}\\{4}\end{array}\right]e^{-t}+\left[\begin{array}{c}{1}\\{1}\\{0}\end{array}\right]e^{2t}$$

24. $${\bf y}=\left[\begin{array}{c}{-2}\\{-2}\\{2}\end{array}\right]e^{2t}-\left[\begin{array}{c}{0}\\{3}\\{0}\end{array}\right]e^{-2t}+\left[\begin{array}{c}{4}\\{12}\\{4}\end{array}\right]e^{4t}$$

25. $${\bf y}=\left[\begin{array}{c}{-1}\\{-1}\\{1}\end{array}\right]e^{-6t}+\left[\begin{array}{c}{2}\\{-2}\\{2}\end{array}\right]e^{2t}+\left[\begin{array}{c}{7}\\{-7}\\{-7}\end{array}\right]e^{4t}$$

26. $${\bf y}=\left[\begin{array}{c}{1}\\{4}\\{4}\end{array}\right]e^{-t}+\left[\begin{array}{c}{6}\\{6}\\{-2}\end{array}\right]e^{2t}$$

27. $${\bf y}=\left[\begin{array}{c}{4}\\{-2}\\{2}\end{array}\right]+\left[\begin{array}{c}{3}\\{-9}\\{6}\end{array}\right]e^{4t}+\left[\begin{array}{c}{-1}\\{1}\\{-1}\end{array}\right]e^{2t}$$

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 $$\left[\begin{array}{c}{1}\\{-1}\end{array}\right]$$, 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 $$\left[\begin{array}{c}{-1}\\{2}\end{array}\right]$$, 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 $$\left[\begin{array}{c}{1}\\{-1}\end{array}\right]$$,$$\left[\begin{array}{c}{-1}\\{1}\end{array}\right]$$, 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 $$\left[\begin{array}{c}{1}\\{-1}\end{array}\right]$$, $$L_{1}$$.

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 $$\left[\begin{array}{c}{-4}\\{1}\end{array}\right]$$, 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 $$\left[\begin{array}{c}{1}\\{-1}\end{array}\right]$$, traversed away from $$L_{1}$$.