Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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These are non-graded practice problems.
Question 19 please!
Transcribed Image Text:8. y(t) = 1²
10. y(t) = e²¹
12. y(t) = cos 3t
In a manner similar to that proposed in Exercises 8-13, verify
the result of Proposition 2.4 for the functions defined in Exer-
cises 14-17.
14. y(t) = t4
16. y(t) = sin 2t
In Exercises 18-25, use Propositions 2.1, 2.4, and 2.7 to trans-
form the given initial value problem into an algebraic equation
involving (y). Solve the resulting equation for the Laplace
transform of y.
9. y(t) = t³
11. y(t) = e 3t
13. y(t) = sin 5t
21. y' - 4y =
18. y' + 3y = t², y(0) = -1
19. y' - 5y = e-2¹, y(0) = 1
20. y' + 5y = t² + 2t + 3, y(0) = 0
15. y(t) = e 2t
17. y(t) = t² + 3t+5
cos 2t, y(0) = -2
22. y" + y = sin 4t, y(0) = 0, y'(0) = 1
23. y" + 2y' + 2y = cos 2t, y(0) = 1, y'(0) = 0
24. y"+y' + 2y = cos 2t + sin 3t, y(0) = -1, y'(0) = 1
-t
25. y" + 3y' + 5y = t + e¹, y(0) = -1, y'(0) = 0
26. y(t) = et sin 3t
28. y(t) = e-2¹ (2t + 3)
In Exercises 26-29, use Proposition 2.12 to find the Laplace
transform of the given function.
30. y(t) = t sin 3t
32. y(t) = t² cos 2t
27. y(t) = e²t cos 2t
29. y(t) = e-t (t² + 3t+4)
In Exercises 30-33, use Proposition 2.14 to find the Laplace
transform of the given function.
31. y(t) = te-t
33. y(t) = t²e²t
In Exercises 34-41, use the propositions in Section 2 to trans-
form the given initial value problem into an algebraic equation
transform of y.
involving L(y). Solve the resulting equation for the Laplace
34. y' + 2y = t sint, y(0) = 1
35. y' - y = 1²e-², y (0) = 0
36. y' + y = e' sin 3t, y(0) = 0
37. y - 2y = e²¹ cost, y(0) = -2
38. y" + 4y = f² sin 4r, y (0) = 0, y' (0) = -1
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