FIND THE LAPLACE TRANSFORM OF THE FOLLOWING USING TABLES OF LAPLACE TRANSFORM AND ITS PROPERTIES. PLEASE SHOW COMPLETE SOLUTIONS AS POSSIBLE. 1. estt3 2. e-2t sin (-) 3. 10t* – sin2t 4. tcos2t 5. 3t* – sin2t 6. t3e-t -St 7. 1+e-5t 8. te2t sin3t 9. tsint 10. tsin5t + 4(-1)² 11. sin (3t + 2)

Q: 8. te2tsin3t

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Q: Use the Laplace transform table to evaluate L'{F(s)}. L' 16s l(s² + 1)* J 5. 7 1. 4. s7 s-a 25 -3 25…

A: Some of the properties of the Inverse Laplace are L-1aF(s)=aL-1F(s) L-1sF(s)=ddt(f(t))+f(0)…

Q: 1. f(t) = e3t 2. f(t) = t3 3. f(t) = cosh(3t) %3D 4. f(t) = cos(2t) 5. f(t) = sin(5t) cos(5t)

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Q: 1 -s F(s) = e = -+ s2 e-3s

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: t2 sin 3t – 3t cos 3t

A: Given :    t2sin3t-3tcos3t

Q: SET UP AND INTEGRATE AND GET TO THE FINAL RESULT FIND THE LAPLACE TRSNSFORM OF THE GIVEN FUNCTION…

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Q: Compute the Laplace transform of the following expressions with Heaviside functions. t H(t - 2) 2.…

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Q: 4. Solve the initial value problem: y" + 3y' – 10y = 0, y(0) = 1, y'(0) = 0 -

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Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 5r…

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Q: 49 2s2 +16 121

A: This is a problem related to inverse laplace transform. Based on the general formula we will answer…

Q: F(s) = -5s (s² + 1)²

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Q: Problem 3. Which gives the inverse transforms of the given s-domain function?…

A: Given problem:-

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y (1) =…

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Q: 6. et+7 dt 7. r'e-)* dt 8. I. 4e-" sin 6t dt

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Q: Find the Laplace transform of: f (t) = t³ – 8t² +1

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Q: b.) 7 ť? e² c) 5 sin 3t - 3 cosh 4t

A: (a) Given that, ft=7t2e2t Therefore, the Laplace transform of ft,…

Q: 1. (t + 2 cos 2t)² – 2 cos²2t

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Q: Have both question and answer, but need help knowing how to get that answer using laplace transform…

A: Given function is,

Q: 5. Find the Fourier transform of of 6e-lt.

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Q: Compute the Inverse Laplace transform of the following signal. (s+1)² s²-s+1 2 Re{s} > 1/12

A: Given,             (s+1)2s2-s+1, Res>12

Q: Solve the shifted data IVP by the Laplace transform. Show the details.

A: We have given a initial value problem, y''-2y'-3y=0 with initial conditions y4=-3, y'4=-17 This is…