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Use the Laplace transform to solve the following initial value problem: y' + 8y = 0 y(0) = 3, y(0) = -2 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 = 0 Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) = + where a < b sta s+b Y(s) = Now by inverting the transform, find y(t) =

Use the Laplace transform to solve the following initial value problem: y' + 8y = 0 y(0) = 3, y(0) = -2 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 = 0 Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) = + where a < b sta s+b Y(s) = Now by inverting the transform, find y(t) =

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/" + 8y = 0 y(0) = 3, 3/(0) =-2 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 = 0 Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) = В s+b where a < b sta Y(s) = + Now by inverting the transform, find y(t)
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y/" + 8y = 0 y(0) = 3, 3/(0) =-2 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 = 0 Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) = В s+b where a < b sta Y(s) = + Now by inverting the transform, find y(t)
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