1. Consider the DE 4y" - 4y' + y = e/2 √√√1 − x² (A) [30%] Find two linearly independent solutions of the DE and the general solution of the homogeneous DE. (B) [70%] Use the variation of parameter method to find the particular solution and write the general solution of the DE.

Q: Solve the differential equation. dy 2√√xy = 1, x, y >0 dx

A: Solution to the Given Differential EquationThe differential equation of the first order is presented…

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A: Step 1: The given vector field is, F=−ϵ Let′s verify the relation ∇⋅F(0,0,0) = limϵ→0+​ volume…

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A: Concave up: the portion of the graph where it opens upwardWe see that the graph opens upward to the…

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A: If you have any questions let me know in the comment box thankyou.

Q: 3. If the total revenue received from the sale of x items is given by R(x)=30ln (2x+1), While the…

A: Let's solve each part step by step.Given:Revenue function: R(x)=30ln(2x+1)Cost function: C(x)=2x​(a)…

Q: 4. Consider the initial value problem y' = 3x(y-1) 1/3, y(xo) = yo. (a) For what points (co, yo)…

A: (Hope this helps)

Q: 8:37 ▬▬▬▬▬▬▬▬▬ Ο Graph of f The figure shows the graph of a periodic function f in the xy-plane.…

A: To determine the frequency of a periodic frunction from a graph, follow the steps below: Step 1:…

Q: Number 19. please show work

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Q: Find integrating factor

A: Problem:Find the integrating factor for the given differential equation:(2xy)dx + (y2 - 3x2)dy = 0.…

Q: Please refer below

A: Step 1: Step 2: Step 3: Here the graph of the function.

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A: Step 1:  Step 2: Step 3: Step 4:

Q: nd ave a ction and ave an 48. The domain of f y=f'(x) x 1 2 (= x<0 x<0 = f(x) possible. Group…

A: (a) Absolute Extrema:Critical Points:f′(x)=0 at x=1f′(x) does not exist at x=2.Boundary…

Q: The graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is…

A: ABC Please feel free to ask doubts.Thank YOU.

Q: Question 11 5+ 4 3 -5-4-3-2-1 2 1 1 2 3 4 5 2345 -4 +-5 + The function graphed above is: Increasing…

A: We have to Identify the increasing and decreasing intervals of the given graph.  Increasing : The…

Q: Calculate sin(10y(2)) where y is the solution of 4.149 12x²y" + 23xy' + 2y : - x such that y(1) = 1,…

A: To solve this problem, follow these steps:Step 1: Solve the Homogeneous EquationThe given…

Q: Given the following graph of the function y = f(x) and n = = 6, answer the following questions about…

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Q: 1. Let Ả = −2x + 3y+42, B = - - 7x +lý +22, and C = −1x + 2y + 42. Find (a) Ả X B (b) ẢX B°C c) →→ Ả…

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Q: 11 fr² Find√² du In(x+u)

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Q: Please find the open intervals where the functions are concave upward or concave downward. Find any…

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Q: ~ exp(10). A 3. Claim number per policy is modelled by Poisson(A) with A sample x of N = 100…

A: (i) A Priori Estimate of the Number of Claims per PolicyWe are given that the prior distribution for…

Q: 7. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.1.505.XP. Evaluate the integral. (Use C for the…

A: Detailed Explanation: Question 7: Question 8: Question 9: Problem3:∫ln⁡(7x+1)dx Question 4:…

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Q: Question 7 4 pts 1 Details The value of China's exports of automobiles and parts (in billions of…

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Q: The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = -4.…

A: To determine the continuity of  f(x)  at  x = -4 , let's analyze the graph: 1. Is  f(-4)  defined?-…

Q: x-4 Let f(x)=5x-1, h(x) = Find (fo h)(0). 3 (fo h)(0) = (Type an integer or a fraction.)

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Q: could you explain this please

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Q: Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: i circled the correct answer could you explain how to get that answer, as well as disprove the other…

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Q: 4.2 Product and Quotient Rules 1. 9(x)=125+1 y14+2 Use the product and/or quotient rule to find the…

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Q: 3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a…

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Q: |x6|= 5 The distance between x and is spaces on the number line, in either direction. Next Part

A: Step 1:|x-6| =5 We know that |x| is x or -x So, here we havex-6 = 5......(1) -(x-6) = 5......(2)…

Q: practice for exam please help

A: To find the derivative of  f(x)=(x3+2x+9)(6+x21​), we use the product rule:  (uv)′=u′v+uv′ Step 1:…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(-3,4, -32) for the function…

A: We have given, The surface equation, f(x,y,z)=0 for the function  f(x,y,z)=ln(−5y−z−4x​)  Step 1 :…

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Q: Find the following limits. (a) lim 3(x-1)² x→2 x (b) lim 0+x (c) lim 3x2-x+1 x²+3 x²+x-12 x-3 x-3

A: (a) limx→2​x3(x−1)2​ Substituting x = 2:  23(2−1)2​=23(1)2​=23​  Therefore: limx→2​x3(x−1)2​=23​…

Q: By using the numbers -5;-3,-0,1;6 and 8 once, find 30

A: Finding 30 Using the Given Numbers We are given the numbers -5, -3, 0, 1, 6, and 8 exactly once, and…

Q: 3.11 (B). A beam, 12 m long, is to be simply supported at 2m from each end and to carry a U.d.l of…

A: Step 1:Step 2: Step 3: Step 4:

Q: Find the derivative of the function. k(x) = − 6(5x +4) -

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Q: Use undetermined coefficients to find the particular solution to y"-3y+2y=4e3 Y(t) =

A: Given the differential equation y''-3y'+2y=4e^3t, we can see that the right-hand side is an…

Q: Explain the key points of Theroem 9.3.6

A: Theorem 9.3.6 is about the general solution of a second order homogeneous linear differential…

Q: PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE A Find the derivative of the function and evaluate f'(x)…

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Q: show work

A: Okay , so here are the solutions. 1. sec²θ - 1Using the identity: sec²θ = 1 + tan²θsec²θ - 1 =…

Q: Find the (perpendicular) distance from the line given by the parametric equations (x(t) = 5+9t y(t)…

A: To find the perpendicular distance from the point P(−1, 1, −3) to the given line, we follow these…

Q: Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties to find…

A: Step 1:  Understanding the Given InformationThe limit values shown below are given to us:…

Q: Qize f(x) x + 2x2 - 2 x² + 4x² - 4 Solve the equation using Newton Raphson

A: Let's solve the system step-by-step using the Newton-Raphson method. # Given system of…

Q: 14. Write u = - sint-cost in the form u = C cos(t - a) with C > 0 and 0 ? PAUSE Z X C VI B N M

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Q: Determine the intervals on which the following function is continuous. f(x) = x - 5x + 6 2 X-9 On…

A: The given function is:f(x)=x2−9x2−5x+6​ Find the values where the denominator is…

Q: Find three horizontal tangents  between [0,10]

A: A horizontal tangent occurs where the derivative of the function is zero, meaning the slope of the…

Q: 38,189 5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of…

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Q: Assuming that the rate of change of the price P of a certain commodity is proportional to the…

A: Step-by-step Explanation:Given the differential equation: dP / dt = k(D - S) Express supply  (S)…