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Use the Laplace transform to solve the following initial value problem: y" +-6y +9y = 0 y(0) = 1, y'(0) = 3 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): Y(s) = Now by inverting the transform, find y(t) = = - 8+a + B (8+a)²

Use the Laplace transform to solve the following initial value problem: y" +-6y +9y = 0 y(0) = 1, y'(0) = 3 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): Y(s) = Now by inverting the transform, find y(t) = = - 8+a + B (8+a)²

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" + 6y +9y = 0 y(0) = 1, y'(0) = 3 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) Y(s) = Now by inverting the transform, find y(t) = = = A + 8+a B (8+a)²
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y" + 6y +9y = 0 y(0) = 1, y'(0) = 3 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) Y(s) = Now by inverting the transform, find y(t) = = = A + 8+a B (8+a)²
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