Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

14.42: Section 8.7 Answers

( \newcommand{\kernel}{\mathrm{null}\,}\)

1. y=12e2t4et+112e2t+2u(t1)(e(t1)e2(t1))

2. y=2e2t+5et+53u(t1)(e(t1)e2(t1))

3. y=16e2t23et12e2t+52u(t1)sinh2(t1)

4. y=18(8cost5sintsin3t)2u(tπ/2)cost

5. y=1cos2t+12sin2t+12u(t3π)sin2t

6. y=4et+3et8+2u(t2)sinh(t2)

7. y=12et72et+2+3u(t6)(1e(t6))

8. y=e2t+7cos2tsin2t12u(tπ/2)sin2t

9. y=12(1+e2t)+u(t1)(e(t1)e2(t1))

10. y=14et+14et(2t5)+2u(t2)(t2)e(t2)

11. y=16(2sint+5sin2t)12u(tπ/2)sin2t

12. y=et(sintcost)e(tπ)sint3u(t2π)e(t2π)sint

13. y=e2t(cos3t+43sin3t)13u(tπ/6)e2(tπ/6)cos3t23u(tπ/3)e2(tπ/3)sin3t

14. y=710e2t65et/212+15u(t2)(e2(t2)e(t2)/2)

15. y=117(12cost+20sint)+134et/2(10cost11sint)u(tπ/2)e(2tπ)/4cost+u(tπ)e(tπ)/2sint

16. y=13(costcos2t3sint)2u(tπ/2)cost+3u(tπ)sint

17. y=etet(1+2t)5u(t1)sinh(t1)+3u(t2)sinh(t2)

18. y=14(etet(1+6t))u(t1)e(t1)+2u(t2)e(t2))

19. y=53sint13sin2t+13u(tπ)(sin2t+2sint)+u(t2π)sint

20. y=34cos2t12sin2t+14+14u(tπ/2)(1+cos2t)+12u(tπ)sin2t+32u(t3π/2)sin2t

21. y=costsint

22. y=14(8e3t12e2t)

23. y=5(e2tet)

24. y=e2t(1+6t)

25. y=14et/2(419t)

29. y=(1)kmω1Recτ/2mδ(tτ) if ω1τϕ=(2k+1)π/2(k= integer )

30.

  1. y=(em+11)(etmet)2(e1),mt<m+1,(m=0,1,)
  2. y=(m+1)sint,2mπt<2(m+1)π,(m=0,1,)
  3. y=e2(tm)e2m+21221e(tm)em+11e1,mt<m+1,(m=0,1,)
  4. y={0,2mπt<(2m+1)π,sint,(2m+1)πt<(2m+2)π,(m=0,1,)

14.42: Section 8.7 Answers is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

Support Center

How can we help?