1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

558 CHAPTER 12 • FOURI ER SERIES AND THE LAPLACE TRANSFORM

y

y = j(t)

0 0

• I 2 3 4 5
  
  
  • I
  
  
  
  

Figure 12.25

14. Let f (t) be as gjven in Figure 12.26. Hint: The function is the integral of the one
    in Exercise 13.

y

y =ft.ti

• I 2 3 4 5

Figure 12. 26

16. Find c-• (1 -e -· -2•)
    82
    
    
    • e.
    
    
    
    

For Exercises 17- 23, solve the initial value problem.

17. y" (t) + 2 y' (t) + 2y (t) = 0, with y (0) = - 1 and y' (0) = 1.

18. y" (t) + 4y' (t) + 5y (t) = 0, with y (0) = 1 and y' (0) = -2.

19. 2y" (t) + 2y' (t) + y (t) = 0, with y (0) = 0 and y' (0) = 1.

20. y"(t)-2y'(t) +y(t) = 2e•, with y(O) = O and y' (0) = O.


21. y" (t) + 2y' (t) + y (t) = 6te-•, with y (0) = 0 and y' (0) = O.

22. y" (t) + 2y' (t) + y (t) = 2U 1 (t) e•-•, with y (0) = 0 and y' (0) = 0.

23. y" (t) + y (t) = Uw/2 (t), with y (0) = 0 and y' (0) = 1.