Page 238 - Schaum's Outline of Differential Equations

CHAP. 21] THE LAPLACE TRANSFORM 221

respectively,

be
2
21.26. Find the Laplace transforms of (a) 6 , (b) cos ad, (c) e sin ad, where a and b denote constants.
Using entries 3 (with n = 3), 9, and 15 of Appendix A with x replaced by 6, we find the Laplace transforms to
be, respectively.

Supplementary Problems

In Problems 21.27 and 21.42, find the Laplace transforms of the given function using Eq. (21.1).

21.27. f(x) = 3

2
21.29. f(x) = e * 21.30. f(x) = e~ 6x
21.31. f(x)=x 21.32. f(x) = -Sx

21.33. f(x) = cos3x 21.34. f(x) = cos4x
21.35. f(x) = cos bx, where b denotes a constant 21.36. f(x)=xe- 8x

bx
21.37. f(x) = xe , where b denotes a constant 21.38. f(x)=x 3

21.41. f(x) in Fig. 21-4 21.42. f(x) in Fig. 21-5

In Problems 21.43 and 21.76, use Appendix A and the Properties 21.1 through 21.6, where appropriate, to find the Laplace
transforms of the given functions.

Fig. 21-4