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

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

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Q: 2. y = sec- (6a2 –- 3x + 2) 3. y = (8x – 6) sin (8x – 6) 4. y = cos- (8x - 4)

A: As per the guidelines, I can solve only first 3 parts. Kindly repost for remaining parts

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A: Solve the integration

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

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A: Given; y=tan(x/3) at x=3.

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A: Answer and explanation is given below

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A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

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Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

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Q: Use variation of parameters to solve y" + y = tan(t). (Note: you might need to use the identity sin²…

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Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

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…