Question

Consider the initial value problem y\" + 16y = cos(3t), y(0) = 4, y'(0) = -4 By applying the Laplace transform to the initial value problem, find the transform of the unique solution of the initial value problem. $\mathcal{L}\{y(t)\} = Solve the initial value problem by finding the inverse Laplace transform. y(t) = \frac{1}{7}cos(3t) + \frac{27}{7}cos(4t) - sin(4t)$

          Consider the initial value problem
y\" + 16y = cos(3t), y(0) = 4, y'(0) = -4
By applying the Laplace transform to the initial value problem, find the transform of the unique
solution of the initial value problem.
$\mathcal{L}\{y(t)\} = 
Solve the initial value problem by finding the inverse Laplace transform.
y(t) = \frac{1}{7}cos(3t) + \frac{27}{7}cos(4t) - sin(4t)$

Consider the initial value problem
y+̈ 16y = cos(3t), y(0) = 4, y'(0) = -4
By applying the Laplace transform to the initial value problem, find the transform of the unique
solution of the initial value problem.
ℒ{y(t)} =
Solve the initial value problem by finding the inverse Laplace transform.
y(t) = (1)/(7)cos(3t) + (27)/(7)cos(4t) - sin(4t)

Added by Clara W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Scott Stetson

09/03/2023

Step 1

$$\mathcal{L}\{y''(t)\} + 16\mathcal{L}\{y(t)\} = \mathcal{L}\{cos(3t)\}$$ Show more…

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Consider the initial value problem $$y'' + 16y = cos(3t), y(0) = 4, y'(0) = -4$$ By applying the Laplace transform to the initial value problem, find the transform of the unique solution of the initial value problem. $$\mathcal{L}\{y(t)\} = $$ Solve the initial value problem by finding the inverse Laplace transform. $$y(t) = \frac{1}{7}cos(3t) + \frac{27}{7}cos(4t) - sin(4t)$$