14.52: Section 10.6 Answers
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1. y=c1e2t[3cost+sint5cost]+c2e2t[3sint−cost5sint]
2. y=c1e−t[5cos2t+sin2t13cos2t]+c2e−t[5sin2t−cos2t13sin2t]
3. y=c1e3t[cos2t+sin2t2cos2t]+c2e3t[sin2t−cos2t2sin2t]
4. y=c1e2t[cos3t−sin3tcos3t]+c2e2t[sin3t+cos3tsin3t]
5. y=c1[−1−12]e−2t+c2e4t[cos2t−sin2tcos2t+sin2t2cos2t]+c3e4t[sin2t+cos2tsin2t−cos2t2sin2t]
6. y=c1[−1−11]e−t+c2e−2t[cos2t−sin2t−cos2t−sin2t2cos2t]+c3e−2t[sin2t+cos2t−sin2t+cos2t2sin2t]
7. y=c1[111]e2t+c2et[−sintsintcost]+c3et[cost−costsint]
8. y=c1[−111]et+c2e−t[−sin2t−cos2t2cos2t2cos2t]+c3e−t[cos2t−sin2t2sin2t2sin2t]
9. y=c1e3t[cos6t−3sin6t5cos6t]+c2e3t[sin6t+3cos6t5sin6t]
10. y=c1e2t[cost−3sint2cost]+c2e2t[sint+3cost2sint]
11. y=c1e2t[3sin3t−cos3t5cos3t]+c2e2t[−3cos3t−sin3t5sin3t]
12. y=c1e2t[sin4t−8cos4t5cos4t]+c2e2t[−cos4t−8sin4t5sin4t]
13. y=c1[−111]e−2t+c2et[sint−costcost]+c3et[−cost−sintsint]
14. y=c1[221]e−2t+c2e2t[−cos3t−sin3t−sin3tcos3t]+c3e2t[−sin3t+cos3tcos3tsin3t]
15. y=c1[121]e3t+c2e6t[−sin3tsin3tcos3t]+c3e6t[cos3t−cos3tsin3t]
16. y=c1[111]et+c2et[2cost−2sintcost−sint2cost]+c3et[2sint+2costcost+sint2sint]
17. y=et[5cos3t+sin3t2cos3t+3sin3t]
18. y=e4t[5cos6t+5sin6tcos6t−3sin6t]
19. y=et[17cos3t−sin3t7cos3t+3sin3t]
20. y=et/2[cos(t/2)+sin(t/2)−cos(t/2)+2sin(t/2)]
21. y=[1−12]et+e4t[3cost+sintcost−3sint4cost−2sint]
22. y=[442]e8t+e2t[4cos2t+8sin2t−6sin2t+2cos2t3cos2t+sin3t]
23. y=[033]e−4t+e4t[15cos6t+10sin6t14cos6t−8sin6t7cos6t−4sin6t]
24. y=[6−33]e8t+[10cos4t−4sin4t17cos4t−sin4t3cos4t−7sin4t]
29. U=1√2[−11],V=1√2[11]
30. U≈[.5257.8507],V≈[−.8507.5257]
31. U≈[.8507.5257],V≈[−.5257.8507]
32. U≈[−.9732.2298],V≈[.2298.9732]
33. U≈[.5257.8507],V≈[−.8507.5257]
34. U≈[−.5257.8507],V≈[.8507.5257]
35. U≈[−.8817.4719],V≈[.4719.8817]
36. U≈[.8817.4719],V≈[−.4719.8817]
37. U=[01],V=[−10]
38. U=[01],V=[10]
39. U=1√2[11],V=1√2[−11]
40. U≈[.5257.8507],V≈[−.8507.5257]