47. y"+3y' + 2y = 4e* 49. y"-4y' + 4y = 2e2x 51. y" + 4y 53. y" + 9y = 2 sec 3x 55. y"+4y 57. You can verify by substitution that ye = complementary function for the nonhome 48. у" - 50. у". 52. y" + 54. y" + 56. у" %3D = cos 3x %3D = sin2 x
47. y"+3y' + 2y = 4e* 49. y"-4y' + 4y = 2e2x 51. y" + 4y 53. y" + 9y = 2 sec 3x 55. y"+4y 57. You can verify by substitution that ye = complementary function for the nonhome 48. у" - 50. у". 52. y" + 54. y" + 56. у" %3D = cos 3x %3D = sin2 x
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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Topic Video
Question
#51 help please
![O File
/home/chronos/u-42c7373e4357ee526bed2268ecc2b0b8f4aed3ab/MyFiles/Downloads/C.%2...
CA
(5) Use the result of part (a) to find a general solution of
24. y3)-y" – 12y = x - 2xe
25. y" + 3y' + 2y = x(e¬* – e-2x)
26. y"- 6y' + 13y = xe3x sin 2x
27. y(4) +5y" + 4y = sin x + cos 2x
28. y(4) +9y" = (x² + 1) sin 3x
29. (D - 1) (D² – 4) y
30. y(4) - 2y" + y = x² cos x
y" + 4y = cos x.
= cos³
%3D
Use trigonometric identities to find general solutions of the
equations in Problems 44 through 46.
= xe* + e2x +e=2x
44. y"+ y' + y = sin x sin 3x
45. y" + 9y = sin
sin x
46. y" +y = x cos" x
Solve the initial value problems in Problems 31 through 40.
31. y" + 4y = 2x; y(0) = 1, y'(0) = 2
32. y" + 3y' + 2y = e*; y(0) = 0, y'(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.
I
%3D
%3D
%3D
196
Chapter 3 Linear Equations of Higher Order
47. y" + 3y' + 2y = 4e*
49. y" - 4y' + 4y = 2e2x
51. y"+ 4y = cos 3x
53. y"+ 9y = 2 sec 3x
55. y" + 4y = sin² x
57. You can verify by substitution that ye = c1x + c2x¬ is a
complementary function for the nonhomogeneous second-
order equation
48. y"-2y'-8y = 3e-2x
50. y" – 4y = sinh 2x
52. y" + 9y = sin 3x
54. y"+y = csc² x
56. y"- 4y = xe*
In Problems 58 through 62, a nonhomogeneous second-order
linear equation and a complementary function ye are given.
Apply the method of Problem 57 to find a particular solution
of the equation.
%3D
58. x2y"- 4xy' + 6y = x³; yc = cx² + c2x³
59. x²y" - 3xy' + 4y = x*; yc = x²(c1 + c2 In x)
60. 4x²y" – 4xy' + 3y = 8x4/3. yc = c]x + c2x3/4
x²y" + xy'-y = 72x°.
61. x2y" + xy' + y = In x; ye =c1 cos(ln x) + c2 sin(In x)
But before applying the method of variation of parame-
ters, you must first divide this equation by its leading co-
%3D
62. (x² – 1) y" – 2xy' + 2y x2 - 1; ye =c1x + c2(1 +x²)
lord form
63. Carry out the solution process indicated in the text to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03106fa3-330c-422f-ad56-a6718a5c3a13%2Fde27afdc-1bb8-4226-af78-d4035344115c%2Fpvpi4ts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:O File
/home/chronos/u-42c7373e4357ee526bed2268ecc2b0b8f4aed3ab/MyFiles/Downloads/C.%2...
CA
(5) Use the result of part (a) to find a general solution of
24. y3)-y" – 12y = x - 2xe
25. y" + 3y' + 2y = x(e¬* – e-2x)
26. y"- 6y' + 13y = xe3x sin 2x
27. y(4) +5y" + 4y = sin x + cos 2x
28. y(4) +9y" = (x² + 1) sin 3x
29. (D - 1) (D² – 4) y
30. y(4) - 2y" + y = x² cos x
y" + 4y = cos x.
= cos³
%3D
Use trigonometric identities to find general solutions of the
equations in Problems 44 through 46.
= xe* + e2x +e=2x
44. y"+ y' + y = sin x sin 3x
45. y" + 9y = sin
sin x
46. y" +y = x cos" x
Solve the initial value problems in Problems 31 through 40.
31. y" + 4y = 2x; y(0) = 1, y'(0) = 2
32. y" + 3y' + 2y = e*; y(0) = 0, y'(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.
I
%3D
%3D
%3D
196
Chapter 3 Linear Equations of Higher Order
47. y" + 3y' + 2y = 4e*
49. y" - 4y' + 4y = 2e2x
51. y"+ 4y = cos 3x
53. y"+ 9y = 2 sec 3x
55. y" + 4y = sin² x
57. You can verify by substitution that ye = c1x + c2x¬ is a
complementary function for the nonhomogeneous second-
order equation
48. y"-2y'-8y = 3e-2x
50. y" – 4y = sinh 2x
52. y" + 9y = sin 3x
54. y"+y = csc² x
56. y"- 4y = xe*
In Problems 58 through 62, a nonhomogeneous second-order
linear equation and a complementary function ye are given.
Apply the method of Problem 57 to find a particular solution
of the equation.
%3D
58. x2y"- 4xy' + 6y = x³; yc = cx² + c2x³
59. x²y" - 3xy' + 4y = x*; yc = x²(c1 + c2 In x)
60. 4x²y" – 4xy' + 3y = 8x4/3. yc = c]x + c2x3/4
x²y" + xy'-y = 72x°.
61. x2y" + xy' + y = In x; ye =c1 cos(ln x) + c2 sin(In x)
But before applying the method of variation of parame-
ters, you must first divide this equation by its leading co-
%3D
62. (x² – 1) y" – 2xy' + 2y x2 - 1; ye =c1x + c2(1 +x²)
lord form
63. Carry out the solution process indicated in the text to
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