The inverse forms of the results in Problem 49 in Exercises 7.1 are and s-a y(t) = (sa)² + b² b (sa)² +6²) = eat cos bt = eat sin bt. Use the Laplace transform and these inverses to solve the given initial-value problem. y' + y = est cos 4t, y(0) = 0
The inverse forms of the results in Problem 49 in Exercises 7.1 are and s-a y(t) = (sa)² + b² b (sa)² +6²) = eat cos bt = eat sin bt. Use the Laplace transform and these inverses to solve the given initial-value problem. y' + y = est cos 4t, y(0) = 0
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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10.
The inverse forms of the results in Problem 49 in Exercises 7.1 are
ℒ−1
= eat cos bt
s − a |
(s − a)2 + b2 |
and
ℒ−1
= eat sin bt.
b |
(s − a)2 + b2 |
Use the Laplace transform and these inverses to solve the given initial-value problem.
y' + y = e−5t cos 4t, y(0) = 0
y(t) =
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