Page 236 - Schaum's Outline of Differential Equations

CHAP. 21] THE LAPLACE TRANSFORM 219

21.22. Find !£{f(x)} for the square wave shown in Fig. 21-2.
This problem can be done two ways,
(a) Note that/(jc) is periodic with period (0=2, and in the interval 0 < x < 2 it can be defined analytically by

From Eq. (21.8), we have

Since

it follows that

(b) The square wave/(jc) also satisfies the equation/!* + 1) = —f(x). Thus, using (_/) of Problem 21.21 with (0=1,
we obtain

Fig. 21-3