3. Find the inverse Laplace transform y(t)=L¹[Y(s)] where 1/6 1/3 Y(s)=e-5s + S s+1 S/2 + 5/3 s² + 4s +6

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: Use Laplace Transform to solve Ø(t) + 2 * cos(t−7)ø(7)dt = e¯¹ for ø(t). -t 0

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Q: Find the Laplace transform of f(t) = cos(2t) * u

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Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: Find the inverse Laplace transform of -6s e F(s) = s2 + 2s – 3 - - (Use for u.(t) .)

A: The given expression is Fs=e-6ss2+2s-3. We have to find the inverse Laplace transform of function…

Q: Find the Laplace transform of f(t) = te-5t.

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Q: Find the inverse Laplace transform of 7s + 3 82 + 17 8 >0

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Q: 7. Use the Laplace transform to solve the difference equation 3x (t) 4x(t-1) = 1, x(t)=0 for t < 0.…

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Q: Find the inverse Laplace transform of F'(s) f(t) = = 6s - 16 s²4s +3

A: The given problem is to find the inverse Laplace transform of the given function F(s). Given F(s)…