Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
need help please for # 47 and 51
Transcribed Image Text:(b) Use the result of part (a) to find a general solution of
24. у(3) — у" — 12y -
25. y" + Зу' + 2у %—D x(е * — е 2х)
26. y" - бу' + 13у %3D хезх sin 2х
27. у(4) + 5у" + 4y
28. y(4) + 9y" = (x² + 1) sin 3x
29. (D — 1)3(D2 — 4)у — хех + е2* + е-2х
30. у(4) — 2у" +у%3
= x – 2xe-3x
y" + 4y = cos³ x.
- e
Use trigonometric identities to find general solutions of the
equations in Problems 44 through 46.
= sin x + cos 2x
44. y" + y' + y = sin x sin 3x
45. у" + 9y%3
46. у" + у %3 х cos3 x
= x² c
= sinª x
´cos x
Solve the initial value problems in Problems 31 through 40.
31. y" + 4y = 2x; y(0) = 1, y'(0) = 2
32. у" + Зу' + 2у %3 е*; у (0) — 0, у' (0) — 3
In Problems 47 through 56, use the method of variation of pa-
rameters to find a particular solution of the given differential
equation.
196
Chapter 3 Linear Equations of Higher Order
47. у" + Зу' + 2у 3 4e*
49. у" — 4у' + 4у %3D 2е2х
51. y" + 4y = cos 3x
53. у" + 9y 3D 2 sec 3x
55. y" + 4y = sin² x
57. You can verify by substitution that yc = c1x +c2x¬1 is a
complementary function for the nonhomogeneous second-
order equation
48. у" — 2у' — 8у — Зе-2х
50. y" – 4y = sinh 2x
52. у" + 9у
54. y" + y = csc² x
56. у" — 4у — хех
In Problems 58 through 62, a nonhomogeneous second-order
linear equation and a complementary function yc are given.
Apply the method of Problem 57 to find a particular solution
of the equation.
= sin 3x
58. x²y" – 4xy' + 6y = x³; yc = c1x² + c2x³
59. x²y" – 3xy' + 4y = x+; yc = x²(c1 + c2 In x)
60. 4x²y" – 4xy' + 3y = 8x4/3; yc = c1x + c2x³/4
x? " + xy' – y = 72x°.
61. x² y" + xy' + y = In x; yc = c1 cos(In x) + c2 sin(ln x)
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