A.8.3: Section 8.3 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. \(y=\frac{1}{100}(3e^{3t}-e^{t/3}(3+310t))\)