Question

Consider the following initial value problem: $y'' - 4y' - 45y = \sin(4t)$ $y(0) = -1$, $y(0) = 6$ Using Y for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L}\{y(t)\}$, find the equation you get by taking the Laplace transform of the differential equation and solve for $Y(s) = \frac{(4s^3 - 2s^2 - 16s - 32)}{(s^2 + 16)(s^2 - 4s - 45)}$

          Consider the following initial value problem:
$y'' - 4y' - 45y = \sin(4t)$
$y(0) = -1$, $y(0) = 6$
Using Y for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L}\{y(t)\}$,
find the equation you get by taking the Laplace transform of the differential equation and solve for
$Y(s) = \frac{(4s^3 - 2s^2 - 16s - 32)}{(s^2 + 16)(s^2 - 4s - 45)}$

Show more…

$Consider the following initial value problem: y” - 4y' - 45y = sin(4t) y(0) = -1, y(0) = 6 Using Y for the Laplace transform of y(t), i.e., Y = ℒ{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) = ((4s^3 - 2s^2 - 16s - 32))/((s^2 + 16)(s^2 - 4s - 45))$

Added by Justin S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/30/2023

Step 1

Step 1: Take the Laplace transform of the given initial value problem: Applying the Laplace transform to the differential equation y'' - 4y' - 45y = sin(4t), we get: s^2Y - sy(0) - y'(0) - 4(sY - y(0)) - 45Y = 4/(s^2 + 16) Simplify this equation to get: s^2Y + Y + Show more…

Show all steps

lock

Thanks for your feedback!

Consider the following initial value problem: y'' - 4y' - 45y = sin(4t), y(0) = -1, y'(0) = 6 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 and solve for Y(s) = Consider the following initial value problem: -4y - 45y = sin(4t), y(0) = -1, y'(0) = 6 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 and solve for Y = 43 - 2s^2 - 16s - 32 / 2 + 16s^2 - 4s - 45

Play audio

Feedback

Powered by NumerAI

Madhur L and 57 other subject Calculus 3 educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later