Use the Laplace transform to solve the following initial value problem: 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 = y" - 4y + 20y = 0 Now solve for Y(s) = By completing the square in the denominator and inverting the transform, find y(t) = y(0) = 0, y'(0) = 4

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use the Laplace transform to solve the following initial value problem:
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
=
y" - 4y + 20y = 0
Now solve for Y(s) =
By completing the square in the denominator and inverting the transform, find
y(t) =
y(0) = 0, y'(0) = 4
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: 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 = y" - 4y + 20y = 0 Now solve for Y(s) = By completing the square in the denominator and inverting the transform, find y(t) = y(0) = 0, y'(0) = 4
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