LESSON 16: SOLUTIONS TO HOMOGENOUS LINEAR DE OF ORDER N. 1. Solve the DE b) y" -9y=0. when x = 0, y = 0, y = -1

Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Evaluate the integuel 99.9 x dv the octant z ≤ 2-y iii) //2₂ i) 0 ii.) - 2 st 1 ivə 1 where OC VJ 4…

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Q: (8) Find the differential for the function using logarithmic differentiation. y = (sin x) (sec): dy…

A: The given function is .The aim is to find the differential for the given function.Formula used:

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Q: The number of bacteria in a culture is increasing according to the law of exponential growth. There…

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Q: Use the Root Test to determine whether the series convergent or divergent. 5n 2n Σ (-20) ³ n+ 1 n =…

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Q: If a 5, b= 7, and c= 11, find the measure of ZC. ZC b C • Enter your answer as a decimal value. •…

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Q: From the list below, select the values of x for which f'(x) > 0. 2 -1 None of the listed x values -3…

A: Given graph of function

Q: -5 -4 -3 -2 5 4 3 2 -1 -1 1 2 4

A: A graph of the function is given.The aim is to find the values of  for which .

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A: Given that Initial Investment = $97,000Lifspan = 9 yearsEstimate Increased = $ 11,000 per yearRate =…

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Q: Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit…

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Q: Find f(x) if f"(x) = 24x²+2x+8, f(0) = 5, f'(1) = -2.

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Q: dz əz Find the values of and at the given point. əx dy z³ - xy + 4yz+y³ - 1 = 0, (5,1,1) əz ax…

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Q: We are interested in the first few Taylor Polynomials for the function f(x) = 5e + 8e-* centered at…

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Q: Consider the following. f(t)= t + cos(t), -2π st≤ 2.T (a) Find the interval of increase. (Enter your…

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Q: Let f(x) and g(x) be differentiable functions. Fill in the blanks with the appropriate function or…

A: To fill in the blanks with appropriate function or expression.Note: Since you have posted multiple…

Q: The BelgeGauffre company builds an ice cream cone from a round waffle of radius 10cm. They start by…

A: The given figure

Q: Determine a mapping of the form (x, y) →_) from y = f(x) for each of the following. y = 3f(2x)…

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Q: ²6² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify…

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Q: 1. Given y" - 2y + 2y = 0 a) Verify that y₁=e* cos x and y₂ = e* sin x are solutions b) Verify that…

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Q: Let (a) 10.5 3.5 ・6.³.5 P f(x) dx = 9, [ r(x) dx = [ 3.5 10.5 a £10.5. f(x) dx = 4, and (b) (8f(x) -…

A: Given,

Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x³ - 6x² +…

A: Consider the function

Q: 2 sin(x) cos(x) + √3 sin(x) = 0 Find all angles in radians that satisfy the equation. For each…

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Q: (1) The critical values of f(x) = 9x + 16x³ + 6x² + 7 are at x = (A) 0 only (B) -1 and 0 (C) -1 and…

A: To find the critical values of .

Q: Find the exact area, in fractional form, under the curve y = 4x³ over the interval [0, 5].

A: we have given function

Q: The position function for a particle's motion on a line is s(t) = t³ -t²-t + 1, t≥ 0, s is in meters…

A: The position function for a particle is .The aim is to find the time  for which the particle is at…

Q: Use the sum of the first eight terms to approximate the sum of the series below. (Round your answer…

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Q: If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median…

A: The objective of the question is to find the difference between the median and the mean of the first…

Q: 2. Determine whether each of the following matrices are in row-echelon form, Reduced row-echelon…

A: A matrix is row echelon matrix if (i) The first non zero element in each non zero row is unity which…

Q: (d) What is >[*\ If (x)| dx? [1500 dx = i

A: Consider the graph

Q: Use spherical coordinates to evaluate the triple integral e-(z²+z²+z²) EV x² + y² + where E is the…

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Q: 0-5-5 x'(t) = -5 0-5 x(t). x( -5 -5 0

A: We have to solve the given initial value problem.

Q: g. Σ. (3) n2 in=1 72

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Q: A. Use the Maclaurin Series with n=4 to approximate cos(2.1) to 4 decimal places. B. Using your…

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Q: person is given an injection of 300 milligrams of penicillin at time t = 0. Let f(t) be the amount…

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables x, y, z)…

A: The given plane equation is To find:- The limits of integration

Q: Solve for x: 3e³-5 = 4 Just enter the number and give a decimal (rounded) answer to 4 places.

A: To solve for .

Q: please provide the answer for part d)

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1,-9, 5) Radius:…

A: To find the standard equation of the sphere with the given characteristics.

Q: dz дz Consider the equation 5 sin (x+y) + 4 sin (x + z) + 5 sin (y + z) = 0. Find the values of and…

A: 5sin⁡(x+y)+4sin⁡(x+z)+5sin⁡(y+z)=0

Q: An object's velocity after t seconds is V(t) Enter an integer or a fraction. DO NOT enter decimals.…

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Q: An elliptic cone in R^3 is described by the equation c^2 = (a + 2)^2 + b^2/9 . a. Find an equation…

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Q: Find the linear approximation for y=sin x at x = 0, and use it to approximate sin(0.3)

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Can you explain how you calculated the partial derivative with respect to s?

A: The total derivative of function  of two variable  is,

Q: Let y = 3e¹ 2x³+e-4z. . Which is y'? You will need to simplify to find the answer.

A: The given function is

Q: Watch Video Given the function f(x) = x55x³, determine all intervals on which f is decreasing.…

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Q: (9) Given that g(x) = e(-), which of the following must be true on the interval (0, ∞)? (A) f(x) is…

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Q: c) y" +10y' + 25y = 0

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

Q: When an object is removed from a furnace and placed in an environment with a constant temperature of…

A: The Newton's cooling law Temperature of the objectProportionality constant Enviornment temperature