Use the Laplace Transform to solve the initial value problem. Show your work. y" – y - 2y = 5 sin x; y(0) = 1, y (0) = -1

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A: I have used the definition of Laplace transformation and calculated the integration

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Q: Fis)-S-65-15 -359

A: Solution is given below:

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A: Given,          f(t)=3sin(bt)cosh(bt)

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A: We have to state true or false The Fourier Transform is particular Laplace transform.

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Q: _-_-7/57 = 1778 ++ (5)) pust

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A: Introduction: The Laplace transformation of sinh(at) and cosh(at) is given by,…

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A: Given f(t)=At

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A: By the method of partial fraction we can solved the problem

Q: Laplace transformation f(t) = e ^ 2t cos2t

A: Laplace transformation f(t) = e ^ 2t cos2t

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Q: erform the Laplace Transform Show your Solution 2e-5t sin 10t + 6e-5t cos 10t

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Q: a. (t-e-4t)² sec²4t -tan 4t]

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Q: Deduce the Fourier transform of -It g(t) = (1+|t|)e-l

A: Given that,  The function is- gt=1+te-t Since, The Fourier transform is defined as Gw=∫-∞∞gte-iwtdt…

Q: FIND INVERSE LAPLACE TRANSFORM, USE THE LAPLACE OF INTEGRALS -7 7. SS+ 2. s+)

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A: Given: Ht-2cosh 6t-2e8t

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Q: 2. f(t) = (t + 2)² et %3D

A: We need to find Laplace Transform of , f(t) = t + 22et We know Laplace Transform is given by , Lf(t)…

Q: estion * he Laplace transform of f (t) = t2 U(t - 3) is: F(s) = e -35 F(s) = e +.

A: Laplace Transform

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Q: - FCS) いは %3D then-L (t" fra) fess %3D

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A: We have to find the partial fraction first.

Q: TT ㅠ (S+T) 2 6) L-¹ {

A: L-1πs+π2 To Do:We have to evaluate the inverse Laplace transform.

Q: -T: TR TR be ormation depined ) =(x+Qy= メ+2y-Zッコメ ec) Rang(T) the

A: Given Linear Transformation:  Tx,y,z=z+2y-z,2x+3y+z,4x+7y-z For kernel we solve homogenous system of…