Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative. f"(z) = 32z –- 18z2 + 8z f(z) =

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A: Given, F'x =fx  fx = 2+4x+5x2   We have to find Fx

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A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

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A: ∫t2+t2 dt

Q: sec 2(t)- 9t2 Justify your response. b. Find the antiderivative of f(t) = s

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Q: Obtain the solution using Integrating Factors Found by Formulas y(y + 2x − 2)dx − 2(x + y)dy = 0

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Q: Obtain the solution using integrating factors found by inspection ydx + 2(y4-x)dy = 0

A: Since you have posted a question with multiple subparts, we will solve the first three sub-parts for…

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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A: Solve the following problem by substitution.

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

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Q: 2х + 3 d |(x² + 3x – 7)7 V

A: Given            ∫2x+3(x2+3x-7)7dx

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Q: Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0

A: As per our guidelines we can answer only 1 question. So kindly repost the remaining questions…

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

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A: Let's find.

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

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Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

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Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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A: For the solution follow the next step.

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A: Please see the answer below

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Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* – x)dy = 0

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A: The given equation is 2yx2-y+xdx+x2-2ydy=0. Solve for the general solution using determination of…

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A: Introduction: The formula for the particular solution by variation of the parameter is given by,…

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Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

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A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: Determine the constant of integration of f (x) = S (15z* – 3x²) dæ if ƒ (1) = 4?

A: