Use the Laplace transform to solve the given integral equation. ƒ'(t) = 1 - sin(t) — ['f(t)dr_ƒ(0)=0 a. f(t)=sin(t)-tsin(t) b. f(t)=- 12e t²e¹ 3te¹ + 4 c. f(t)=sin(t) + cos(t) d. f(t) = 47 + 17 f(t) = e-¹ 8 64sin(√17t) 17√17 3t 27sin(√10t) 0/00

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A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

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A: Given:

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A: Answer and explanation is given below

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Q: Find the derivative of the function. y = [x + (x + sin²(x))6]4 2 63 y' = 4 x + x + sin x • 1+4 x +…

A: Please see the attached image for the solution.Note that a series of Chain Rule for Differentiation…