Use the Laplace transform to solve the following initial value problem: 2y" +4/ + 18y = 2 cos(3t), y(0) = 0, y (0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. L{y(t)}(s) b. Express the solution y(t) in terms of a convolution integral. y(t) = dw
Use the Laplace transform to solve the following initial value problem: 2y" +4/ + 18y = 2 cos(3t), y(0) = 0, y (0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. L{y(t)}(s) b. Express the solution y(t) in terms of a convolution integral. y(t) = dw
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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Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: 2y" +4/ + 18y = 2 cos(3t), y(0) = 0,
y (0) = 0.
a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}.
Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral.
L{y(t)}(s)
b. Express the solution y(t) in terms of a convolution integral.
y(t) =
dw
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