Use the Laplace transform to solve the following initial value problem: y" = 2, y(0) = 4, y'(0) = -3. (1) First, using Y for the Laplace transform of y(t), i.e., Y = = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) = = 0
Use the Laplace transform to solve the following initial value problem: y" = 2, y(0) = 4, y'(0) = -3. (1) First, using Y for the Laplace transform of y(t), i.e., Y = = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) = = 0
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 8CR
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![Use the Laplace transform to solve the following initial value problem: y" = 2, y(0) = 4, y' (0) = −3.
(1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)),
find the equation you get by taking the Laplace transform of the differential equation to obtain
(2) Next solve for Y =
(3) Finally apply the inverse Laplace transform to find y(t)
y(t) =
= 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa59e6cdd-e364-4367-9996-bee45d6f7a4b%2Feba2e51a-2994-47c9-b939-dc4e31cbbf80%2Fn8dvm1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y" = 2, y(0) = 4, y' (0) = −3.
(1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)),
find the equation you get by taking the Laplace transform of the differential equation to obtain
(2) Next solve for Y =
(3) Finally apply the inverse Laplace transform to find y(t)
y(t) =
= 0
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