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14.38: Section 8.3 Answers

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Aug 11, 2020
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- 14.37: Section 8.2 Answers
- 14.39: Section 8.4 Answers

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1. $y=\frac{1}{6}e^{t}-\frac{9}{2}e^{-t}+\frac{16}{3}e^{-2t}$

2. $y=-\frac{1}{3}+\frac{8}{15}e^{3t}+\frac{4}{5}e^{-2t}$

3. $y=-\frac{23}{15}e^{-2t}+\frac{1}{3}e^{t}+\frac{1}{5}e^{3t}$

4. $y=-\frac{1}{4}e^{2t}+\frac{17}{20}e^{-2t}+\frac{2}{5}e^{3t}$

5. $y=\frac{11}{15}e^{-2t}+\frac{1}{6}e^{t}+\frac{1}{10}e^{3t}$

6. $y=e^{t}+2e^{-2t}-2e^{-t}$

7. $y=\frac{5}{3}\sin t-\frac{1}{3}\sin 2t$

8. $y=4e^{t}-4e^{2t}+e^{3t}$

9. $y=-\frac{7}{2}e^{2t}+\frac{13}{3}e^{t}+\frac{1}{6}e^{4t}$

10. $y=\frac{5}{2}e^{t}-4e^{2t}+\frac{1}{2}e^{3t}$

11. $y=\frac{1}{3}e^{t}-2e^{-t}+\frac{5}{3}e^{-2t}$

12. $y=2-e^{-2t}+e^{t}$

13. $y=1-\cos 2t+\frac{1}{2}\sin 2t$

14. $y=-\frac{1}{3}+\frac{8}{15}e^{3t}+\frac{4}{5}e^{-2t}$

15. $y=\frac{1}{6}e^{t}-\frac{2}{3}e^{-2t}+\frac{1}{2}e^{-t}$

16. $y=-1+e^{t}+e^{-t}$

17. $y=\cos 2t-\sin 2t+\sin t$

18. $y=\frac{7}{3}-\frac{7}{2}e^{-t}+\frac{1}{6}e^{3t}$

19. $y=1+\cos t$

20. $y=t+\sin t$

21. $y=t-6\sin t+\cos t+\sin 2t$

22. $y=e^{-t}+4e^{-2t}-4e^{-3t}$

23. $y=-3\cos t-2\sin t+e^{-t}(2+5t)$

24. $y=-\sin t-2\cos t+3e^{3t}+e^{-t}$

25. $y=(3t+4)\sin t-(2t+6)\cos t$

26. $y=-(2t+2)\cos 2t+\sin 2t+3\cos t$

27. $y=e^{t}(\cos t-3\sin t)+e^{3t}$

28. $y=-1+t+e^{-t}(3\cos t-5\sin t)$

29. $y=4\cos t-3\sin t-e^{t}(3\cos t-8\sin t)$

30. $y=e^{-t}-2e^{t}+e^{-2t}(\cos 3t- 11/3\sin 3t)$

31. $y=e^{-t}(\sin t-\cos t)+e^{-2t}(\cos t+4\sin t)$

32. $y=\frac{1}{5}e^{2t}-\frac{4}{3}e^{t}+\frac{32}{15}e^{-t/2}$

33. $y=\frac{1}{7}e^{2t}-\frac{2}{5}e^{t/2}+\frac{9}{35}e^{-t/3}$

34. $y=e^{-t/2}(5\cos (t/2)-\sin (t/2))+2t-4$

35. $y=\frac{1}{17}(12\cos t+20\sin t-3e^{t/2}(4\cos t+\sin t))$

36. $y=\frac{e^{-t/2}}{10}(5t+26)-\frac{1}{5}(3\cos t+\sin t)$

37. $y=\frac{1}{100}(3e^{3t}-e^{t/3}(3+310t))$

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