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...
Related questions
Question
Do problems 32, 35, 36, 42
![39. 2y" + Зу" — 3у' — 2у — е ", У(O) — 0, у'(0) — 0,
y"(0) = 1
-
40. у" + 2y" — у' — 2у 3D sin 3t, у(0) — 0, у'() — 0,
y"(0) = 1
The inverse forms of the results are
S - a
L-
(s — а)? + b?
= ea' cos bt
L-1.
(s
eat sin bt.
a)? + b? ]
In Problems 41 and 42 use the Laplace transform and these
inverses to solve the given initial-value problem.
-3t
41. у' + у 3 е cos 2r, y(0) — 0
42. у" — 2у' + 5у %3D 0, у(0) %3 1, у'(0) %3 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b89a09c-6e39-4856-860f-296a7674c0ed%2F9c29c0ee-7350-418a-9745-c56fc0e77201%2Fapjb9nq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:39. 2y" + Зу" — 3у' — 2у — е ", У(O) — 0, у'(0) — 0,
y"(0) = 1
-
40. у" + 2y" — у' — 2у 3D sin 3t, у(0) — 0, у'() — 0,
y"(0) = 1
The inverse forms of the results are
S - a
L-
(s — а)? + b?
= ea' cos bt
L-1.
(s
eat sin bt.
a)? + b? ]
In Problems 41 and 42 use the Laplace transform and these
inverses to solve the given initial-value problem.
-3t
41. у' + у 3 е cos 2r, y(0) — 0
42. у" — 2у' + 5у %3D 0, у(0) %3 1, у'(0) %3 3
![2 TRANSFORMS OF DERIVATIVES
In Problems 31–40 use the Laplace transform to solve the
given initial-value problem.
dy
31.
dt
у %3D 1, у(0) — 0
dy
32. 2 + у %3D 0, у(0)
dt
|
33. y' + бу %3Dett, y(0) 3D 2
34. y' — у 3D 2 cos 5t, y(0) %3D 0
35. y" + 5у' + 4у %3D 0, у(0) — 1, у'(0) 3D 0
36. y" – 4y'
3 безг —
Зе ", у0) — 1, у'(0) — —1
Vz sin V2r,
37. у" + у %3D у(0) %3D 10, у'(0) — 0
38. у" + 9у %3D е, у(0) 3D 0, у'(0) 3D 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b89a09c-6e39-4856-860f-296a7674c0ed%2F9c29c0ee-7350-418a-9745-c56fc0e77201%2F1hweigg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2 TRANSFORMS OF DERIVATIVES
In Problems 31–40 use the Laplace transform to solve the
given initial-value problem.
dy
31.
dt
у %3D 1, у(0) — 0
dy
32. 2 + у %3D 0, у(0)
dt
|
33. y' + бу %3Dett, y(0) 3D 2
34. y' — у 3D 2 cos 5t, y(0) %3D 0
35. y" + 5у' + 4у %3D 0, у(0) — 1, у'(0) 3D 0
36. y" – 4y'
3 безг —
Зе ", у0) — 1, у'(0) — —1
Vz sin V2r,
37. у" + у %3D у(0) %3D 10, у'(0) — 0
38. у" + 9у %3D е, у(0) 3D 0, у'(0) 3D 0
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