. Find the Laplace Transform of the following. i.y" + y = 8(t – 2n), y(0) = 10, y'(0) = 0 %3D ii.y" – y = 108 (t -;) – 1008(t – 1), y(0) = 10, y'(0) = 1 %3D

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A: Given f(t) = cos(2t) + 7sin(2t)

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Q: What is the initial value of f(t) if its Laplace transform is 5-2? 2s(s+2)

A: To Find: The initial value of f(t) if its Laplace transform is s-22ss+2

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A: Some of the properties of Inverse Laplace For the function f(t) and a is some constant ,…

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Q: Find the Laplace transform for -4 f(t) = e'sin2t + e¯'cost 2 s + 1 2 s + 1 + s + 2s + 5 s - 2s + 2 2…

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Q: I. Find the Laplace transform of the following functions: 1. 2 e3t sin 2t - 3 e3t cos 2t 2. t2 sin…

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Q: Give the Laplace transform of the solution to y' + 3y-4 e* – 2 sin(2 x), y(0)=5]

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Q: 1. A) Evaluate the integral (e*(1+t sint)dt by using Laplace transform definition and properties of…

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Q: Find the Laplace Transform of h(t) = t? sin(2t) 12s?– 16 A H(s) (s²+4) 3 48² – 3 B H(s) (s² – 4) 3…

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Q: Find the Laplace Transform of y in the differential equation (D2 + 5D + 3)y = 10 Assuming the…

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Q: O fe) = e* cos 2t -t * + Gn 状 - as )

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Q: 1. Use the Laplace transform to solve the IVP: y" – 4y' = 6e3t – 3e¬t, y(0) = 1, y (0) = –1 %3D

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Q: You have a Laplace transform of the form Y (s) = -DG+2) + F6+3) e -e-2s s²(s+3) S 1 (s-1)(s+2) To…

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A: Solution: Given ivp is

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Q: Compute for the inverse Laplace transform of Y (s) = (s+2)³ * 3 e-2t+2 e-2tt e-2442

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Q: Consider the following IVP: y"-3y'-10 y=1, y(0)=-1.y'(0)=2 (a) Find the Laplace transform of the…

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Q: 2. Find L{e3t cos 2t} using property of Laplace transform

A: We’ll answer the first question (Question number 2) since the exact one wasn’t specified. Please…

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Q: What is the inverse Laplace transform of Y (s) = (4s + 4)/ (s2 + 4s + 13)

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Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

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Q: C- Using Laplace transform, find the solution of the following problem. d?y +y = 3 cos2t dt2 subject…

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Q: 1. Determine the inverse Laplace transform of the function below. 10 G(s) = (s + 1)(s2 + 4s + 13) 2.…

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Q: Use laplace transform to find the initial value problem; a) y''+2y=alpha(t-1),y(0)=0,y'(0)=1

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Q: Q1\ Find the Z-transform of A) cosh ( +a} B)는 u(k) pk = e" 00 where Lk=0 k! k!

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Q: 4)Use Laplace transform to solve y +2y +2y=e", y(0) = 2, y'(0) = -1

A: Given y"+2y'+2y=e-t , y0=2 , y'0=-1 Ly"=s2Ly-sy0-y'0 Ly'=s Ly-y0 Le-t=1s+1 Now…

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Q: 2. Use Laplace transform to solve | cos(4t), 0T y" + 16y = ; y(0) = 0, y'(0) = 1.

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Q: Find the Laplace Transform ofe 2 cos3t + 5e21 sin3t s+2 15 A g2+9 s2+9 (s+ 2) + 15 в (s2+4s) + 13 15…

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