### Laplace Transform of Initial Value Problem**Problem Statement:**Find the Laplace transform \( Y(s) \) of the solution \( y(t) \) of the initial value problem\[ y'' + 4y = 0, \]\[ y(0) = 0, \]\[ y'(0) = 2. \]You do not have to take the inverse Laplace transform to solve for \( y(t) \).

Apply Laplace transform on both sides

Answered: 2. Find the Laplace transform Y(s) of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. Laplace Transform. Please show your complete solution
4- Inversely transform, L^-1, the following function with inverse transform of Laplace. (Check attached image) a) Data: Identify the coefficients, constants and/or initial conditions that are provided in the problem. Also, write down those functions that must be determined. b) Fundamentals: Explain the procedure, seen that leads to obtaining the inverse Laplace transform L^-1[Y(s)] = y(t). c) Argumentation/Development: Develop the necessary transformations to obtain y(t). d) Result: Write down the transform y(t).
y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives
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2. Find the Laplace transform Y(s) of the solution y(t) of the initial value problem y"+4y=0, y(0)=0, y'(0)=2 You do not have to take the inverse Laplace transform to solve for y(t).