. 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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Q: Find the Laplace Transform of the following periodic functions (47² s² – 2)e²** +4 as +2 s'(e** -1)…

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Q: 1. FIND THE LAPLACE TRANSFORM OF THE FOLLOWING EXPRESSIONS: 1.1.1 +et+t+ sint + cost - sinht + cosht…

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Q: 8. Find the Fourier transform of the following functions sin(57x) a. π.χ

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Q: (1- cos 2wt) where w is a positive constant WHAT IS THE LAPLACE TRANSFORM OF THIS?

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Q: -7s 4s +7 Q5.A.i. Find the inverse Laplace transform of F(s)= (s – 4)° – 21 (s+1X2s + 3)(3s +5)

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Q: Find the inverse Laplace transform of y= s2+ 25 O a. 2cos (5t) O b. 1 -sin (5t) O c. none of the…

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

Q: Part II. Solve the following IVP using Laplace Transform: 1. 4y" + y' + 5y = 0 y(0) = 2 y' (0) = 1…

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Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2). (b)…

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Q: 8. Find the function whose Fourier sine transform is the following function. S[u] - 2 0 x = [1, 2],…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin(V2t), y(0) = 11,…

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Q: Find the Inverse Laplace Transform of the following functions 3s? – 2s–1 (s- 3)(s² +1) A) F(s) =…

A: As Multiple Questions are given , I will solve the first one Only :   We are given…

Q: b) f(t) = 3 sin(2t) + 5e³t so

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Q: d³y d²y 3 dx3 3 – y = x²e*; y(0) = 1, y'(0) = 2, y"(0) = 3 dy dx2 dx

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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: 12. F(s) (s-4)2 A. 2 cosh 2t B. t cosh 2t C. te* D.t sinh 2t

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Q: 7. F(t) = cos?- sin? 2 8. F(t) = cos ( bt 9. F(t) = 8 sin- cos %3D

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Q: Using Laplace transform, sole cỳ"+y= cos x, where y (0) = 0 = y'(0)

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Q: 9.) The Inverse Laplace tra (A) In(s² - 2-3 (C) //e+ + 3/e³1

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Q: ) If F(ƒ) = ƒ(§) is the Fourier transform of f(x), show that the Fourier transform of x f(x) is…

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Q: Determine the Fourier transform of the following signal: _(t+1) u(t+1) x (t) = è

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Q: (5) y'(t) =1– sint – | y (u)du, y(0) =0

A: We have to find General Solution of given differential equation using Laplace transform Method.