Use the Laplace transform to solve the given initial-value problem.y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1y(t) = Use Definition 7.1.1,DEFINITION 7.1.1 Laplace TransformLet f be a function defined for t 2 0. Then the integralLe-stf(t) dtis said to be the Laplace transform of f, provided that the integral converges.to find L{f(t)}. (Write your answer as a function of s.)Scos(t),f(t)0 πL{f(t)} =(s > 0)

Given: Given initial value problem is y'''+2y''-y'-2y=sin4t,y0=0,y'0=0,y''0=1

Answered: Use the Laplace transform to solve the…

Use the Laplace transform to solve the given initial-value problem. y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1 y(t) =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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Question

Use the Laplace transform to solve the given initial-value problem.

y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1

y(t) =

Use Definition 7.1.1,
DEFINITION 7.1.1 Laplace Transform
Let f be a function defined for t 2 0. Then the integral
L
e-stf(t) dt
is said to be the Laplace transform of f, provided that the integral converges.
to find L{f(t)}. (Write your answer as a function of s.)
Scos(t),
f(t)
0 <t< n
0,
t >π
L{f(t)} =
(s > 0)

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