14.38: 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))