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11.5: A.10.4 Section 10.4 Answers

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    Dec 31, 2022
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1. y=c1[11]e3t+c2[1−1]e−t

2. y=c1[11]e−t/2+c2[−11]e−2t

3. y=c1[−31]e−t+c2[−12]e−2t

4. y=c1[21]e−3t+c2[−21]et

5. y=c1[11]e−2t+c2[−41]e3t

6. y=c1[32]e2t+c2[11]et

7. y=c1[−31]e−5t+c2[−11]e−3t

8. y=c1[121]e−3t+c2[−1−41]e−t+c3[−1−11]e2t

9. y=c1[212]e−16t+c2[−120]e2t+c3[−101]e2t

10. y=c1[−2−43]et+c2[−110]e−2t+c3[−7−54]e2t

11. y=c1[−1−11]e−2t+c2[−1−21]e−3t+c3[−2−63]e−5t

12. y=c1[1171]e3t+c2[121]e−2t+c3[111]e−t

13. y=c1[4−11]e−4t+c2[−1−11]e6t+c3[−101]e4t

14. y=c1[115]e−5t+c2[−101]e5t+c3[110]e5t

15. y=c1[1−12]+c2[−103]e6t+c3[130]e6t

16. y=−[26]e5t+[42]e−5t

17. y=[2−4]et/2+[−21]et

18. y=[77]e9t−[24]e−3t

19. y=[39]e5t−[42]e−5t

20. y=[550]et/2+[001]et/2+[−120]e−t/2

21. y=[333]et+[−2−22]e−t

22. y=[2−22]et−[303]e−2t+[110]e3t

23. y=−[121]et+[424]e−t+[110]e2t

24. y=[−2−22]e2t−[030]e−2t+[4124]e4t

25. y=[−1−11]e−6t+[2−22]e2t+[7−7−7]e4t

26. y=[144]e−t+[66−2]e2t

27. y=[4−22]+[3−96]e4t+[−11−1]e2t

29. Half lines of L1:y2=y1 and L2:y2=−y1 are trajectories other trajectories are asymptotically tangent to L1 as t→−∞ and asymptotically tangent to L2 as t→∞.

30. Half lines of L1:y2=−2y1 and L2:y2=−y1/3 are trajectories other trajectories are asymptotically parallel to L1 as t→−∞ and asymptotically tangent to L2 as t→∞.

31. Half lines of L1:y2=y1/3 and L2:y2=−y1 are trajectories other trajectories are asymptotically tangent to L1 as t→−∞ and asymptotically parallel to L2 as t→∞.

32. Half lines of L1:y2=y1/2 and L2:y2=−y1 are trajectories other trajectories are asymptotically tangent to L1 as t→−∞ and asymptotically tangent to L2 as t→∞.

33. Half lines of L1:y2=−y1/4 and L2:y2=−y1 are trajectories other trajectories are asymptotically tangent to L1 as t→−∞ and asymptotically parallel to L2 as t→∞.

34. Half lines of L1:y2=−y1 and L2:y2=3y1 are trajectories other trajectories are asymptotically parallel to L1 as t→−∞ and asymptotically tangent to L2 as t→∞.

36. Points on L2:y2=y1 are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of L1, parallel to [1−1], traversed toward L1.

37. Points on L1:y2=−y1/3 are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of L1, parallel to [−12], traversed away from L1.

38. Points on L1:y2=y1/3 are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of L1, parallel to [1−1],[−11], traversed away from L1.

39. Points on L1:y2=y1/2 are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of L1, parallel to [1−1], L1.

40. Points on L2:y2=−y1 are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of L2, parallel to [−41], traversed toward L1.

41. Points on L1:y2=3y1 are trajectories of constant solutions. The trajectories of nonconstant solutions are half-lines on either side of L1, parallel to [1−1], traversed away from L1.

This page titled 11.5: A.10.4 Section 10.4 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

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