Page 265 - Schaum's Outline of Differential Equations

248 SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS [CHAP. 24

or

Then using Appendix A, entries 17 and 9 with a = 4 and t replacing x, we obtain

Compare with the results of Problem 1410.

Supplementary Problems

Use Laplace transforms to solve the following problems.

24.17. y' + 2y = 0; y(0) = 1 24.18. y' + 2y = 2;y(0) = l
x
y
24.19. y' + 2y = e ; y(0) = 1 24.20. y' + 2y = 0; (l) = 1
sx
24.21. y' + 5y = 0; (l) = 0 24.22. y'-5y = e ; y(0) = 2
y
x
24.23. y' + y = xe~ ; y(0) = -2 24.24. y' + y = sin x
24.25. y' + 20y = 6 sin 2x; y(0) = 6 24.26. y" - y = 0; y(0) = 1, /(O) = 1
I
24.27. y" -y = sin x; y(0) = 0, y'(0) = 1 24.28. /'- 3, = e ;XO) = L/(0) = 0
24.29. y" + 2y' -3y = sin 2x; y(0) = /(O) = 0 24.30. y" + y = sin x; y(0) = 0, /(O) = 2

24.31. y" + y' + y = 0; y(0) = 4, /(O) = -3 24.32. /' + 2y' + 5y = 3e^; y(G) = 1, /(O) = 1
24.33. y" + 5y' -3y = u(x - 4); y(0) = 0, y'(0) = 0 24.34. y" + y = 0; y(n) = 0, y'(n) = -1

4
24.35. y'" ~y = 5; y(G) = 0, /(O) = 0, /'(O) = 0 24.36. / > -y = 0; y(0) = 1, /(O) = 0, /'(O) = 0, /"(O) = 0