Question

Given the second order initial value problem y'' - 4y = 4?(t - 3), y(0) = -1, y'(0) = 2 Let Y(s) denote the Laplace transform of y. Then Y(s) = Taking the inverse Laplace transform we obtain y(t) =

          Given the second order initial value problem y'' - 4y = 4?(t - 3), y(0) = -1, y'(0) = 2
Let Y(s) denote the Laplace transform of y. Then
Y(s) =
Taking the inverse Laplace transform we obtain
y(t) =

Added by Kathy H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/25/2023

Step 1

The Laplace transform of y''(t) is s^2Y(s) - sy(0) - y'(0), and the Laplace transform of 4y(t) is 4Y(s). The Laplace transform of 48(t-3) is 48e^{-3s}/s. Now, we can substitute these into the given equation: s^2Y(s) - sy(0) - y'(0) - 4Y(s) = 48e^{-3s}/s Now, Show more…

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Given the second order initial value problem y'' - 4y = 4̈́(t - 3), y(0) = -1, y'(0) = 2 Let Y(s) denote the Laplace transform of y. Then Taking the inverse Laplace transform we obtain y(t) = Y(s) =