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Inverse Laplace Transform of Rational Functions:

6sÂ² + 50

Find the inverse Laplace transform of the function given: f(t) = (2s + 4)/(s + 3)

Answer: f(t) = 2cos(2t) + 3sin(2t) + e^(-3t)

Initial Value Problem:

Find the inverse Laplace transform of the following function:

dy/dx + 4y + 4y = e^(-t)

y(0) = 2 and y'(0) = 3.

Answer:

1. y(t) = 3e^(-3t) + 3t + 4e^(-t)

2. y(t) = 3e^(-3t) + 3t + 2e^(-t)

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04:40

Find the inverse Laplace of the given function of $ F(s) = 53 + 452 flt) = e^{-4t}+4t-1(e^{-4t}+4t+1) 16 f(t) g(e^{-4t}-4t -1)flt) (e^{-4t}-4t-1) 16QUESTION 6Solve the given differential equation by using Laplace Transforms. The function is subject to the given condition/conditions (boundary/initial condition/conditions) y”’ +2y +y=2, initial conditions y(0) =0, y'(0) =0, y”(0) =2(1-e^{-t}) – te^{-t} + e^{-t} – te^{-t} + 2-2e^{-t} – te^{-t}.

06:58

Find the inverse Laplace transform of the following:G(s) 82 + [5+13Solve the following initial-value problems with Laplace transforms 0<t< 1(a) % + 2y = f(t). y(o) = 2 f(t)1 <t< 24 + It,t22(6) !” + 2y’ + %y = 8t 31. “(0) = 1. 4() =1

01:24

Determine the Inverse Laplace Transform for the following function:f(t) = 2e^(-3t)sin(2t) + 6e^3tcos(2t) + 4e^(-1/2)sin(2t) + e^(3t)sin(2t)

02:46

Linear Property of Inverse Laplace Transform: -25+4Find the inverse Laplace transform of the function given, f(t) = 3s^2 + 6Answer: f(t) = Zcos(Vz) + 24Esin(Vz)

First shift Property of Inverse Laplace Transform: 6 -$ Find the inverse Laplace transform of the function given, f(t) = 5t + 25 + 2Answer: f(t) = Te^(-t)sin(t) – e^(-t)cos(t)

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