Page 234 - Schaum's Outline of Differential Equations

CHAP. 21] THE LAPLACE TRANSFORM 217

and

21.17. Find
Let/(jc) = x cos 2x. From entry 13 of Appendix A with a = 2, we obtain

Then, from Property 21.2 with a = —1,

21.18. Find

Define f(x) = • Then and, from entry 4 of Appendix A, we obtain

It now follows from Property 21.3 with n = 3 that

which agrees with entry 6 of Appendix A for n = 4.

21.19. Find

Taking/(X) = sin 3x, we find from entry 8 of Appendix A with a = 3 that

Then, using Property 21.4, we obtain

21.20. Find

Taking f(t) = sinh 2t, we have f(x) = sinh 2x. It now follows from entry 10 of Appendix A with a = 2 that