14.42: Section 8.7 Answers
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1. y=12e2t−4e−t+112e−2t+2u(t−1)(e−(t−1)−e−2(t−1))
2. y=2e−2t+5e−t+53u(t−1)(e(t−1)−e−2(t−1))
3. y=16e2t−23e−t−12e−2t+52u(t−1)sinh2(t−1)
4. y=18(8cost−5sint−sin3t)−2u(t−π/2)cost
5. y=1−cos2t+12sin2t+12u(t−3π)sin2t
6. y=4et+3e−t−8+2u(t−2)sinh(t−2)
7. y=12et−72e−t+2+3u(t−6)(1−e−(t−6))
8. y=e2t+7cos2t−sin2t−12u(t−π/2)sin2t
9. y=12(1+e−2t)+u(t−1)(e−(t−1)−e−2(t−1))
10. y=14et+14e−t(2t−5)+2u(t−2)(t−2)e−(t−2)
11. y=16(2sint+5sin2t)−12u(t−π/2)sin2t
12. y=e−t(sint−cost)−e−(t−π)sint−3u(t−2π)e−(t−2π)sint
13. y=e−2t(cos3t+43sin3t)−13u(t−π/6)e−2(t−π/6)cos3t−23u(t−π/3)e−2(t−π/3)sin3t
14. y=710e2t−65e−t/2−12+15u(t−2)(e2(t−2)−e−(t−2)/2)
15. y=117(12cost+20sint)+134et/2(10cost−11sint)−u(t−π/2)e(2t−π)/4cost+u(t−π)e(t−π)/2sint
16. y=13(cost−cos2t−3sint)−2u(t−π/2)cost+3u(t−π)sint
17. y=et−e−t(1+2t)−5u(t−1)sinh(t−1)+3u(t−2)sinh(t−2)
18. y=14(et−e−t(1+6t))−u(t−1)e−(t−1)+2u(t−2)e−(t−2))
19. y=53sint−13sin2t+13u(t−π)(sin2t+2sint)+u(t−2π)sint
20. y=34cos2t−12sin2t+14+14u(t−π/2)(1+cos2t)+12u(t−π)sin2t+32u(t−3π/2)sin2t
21. y=cost−sint
22. y=14(8e3t−12e−2t)
23. y=5(e−2t−e−t)
24. y=e−2t(1+6t)
25. y=14e−t/2(4−19t)
29. y=(−1)kmω1Re−cτ/2mδ(t−τ) if ω1τ−ϕ=(2k+1)π/2(k= integer )
30.