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Use the Laplace transform to solve the following initial value problem: y' + 3y = 0 y(0) = 4, y (0) = 1 a. 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 = 0 b. Now solve for Y(s) = c. Write the above answer in its partial fraction decomposition, Y(s) = where a < b Y(s) = d. Now by inverting the transform, find y(t) = ■. A B + s+a s+b =+

Use the Laplace transform to solve the following initial value problem: y' + 3y = 0 y(0) = 4, y (0) = 1 a. 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 = 0 b. Now solve for Y(s) = c. Write the above answer in its partial fraction decomposition, Y(s) = where a < b Y(s) = d. Now by inverting the transform, find y(t) = ■. A B + s+a s+b =+

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the Laplace transform to solve the following initial value problem: y" + 3y = 0 y(0) = 4, y(0) = 1 a. 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 = 0 b. Now solve for Y(s) = c. Write the above answer in its partial fraction decomposition, Y(s) = where a < b Y(s) = [ d. Now by inverting the transform, find y(t) = ■. A B s+a s+b Il+ +
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y" + 3y = 0 y(0) = 4, y(0) = 1 a. 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 = 0 b. Now solve for Y(s) = c. Write the above answer in its partial fraction decomposition, Y(s) = where a < b Y(s) = [ d. Now by inverting the transform, find y(t) = ■. A B s+a s+b Il+ +
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