Using the method of Laplace Transform solve the given IVP y'' - 2y' + 2y = \cos t; y(0) = 1....

Question:

Using the method of Laplace Transform solve the given IVP

{eq}\displaystyle y'' - 2y' + 2y = \cos t; \quad y(0) = 1, \quad y'(0) = 0 {/eq}

Laplace Transform to Solve IVP:

A linear differential equation with initial conditions given can be solved by using Laplace transform method.

The differential equation in time domain gets converted into an algebraic equation in frequency domain.

This equation can easily be solved using rules of algebra and the time domain solution can be found using inverse Laplace transforms.

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The given equation is {eq}y''-2y'+2y=\cos t {/eq}

Take Laplace transform of both sides and apply initial conditions.

{eq}\begin{align} \left[...

First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.