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Consider the difference equation Consider the difference equation Find the explicit solution of this difference equation in terms of y<sub>0</sub> . A) y_{n}=-0.55 n y_{0}, n=0,1,2,3 \ldots B) y_{n}=(-0.55) ^{n} y_{0}, n=0,1,2,3 \ldots C) y_{n}=-0.55^{n} y_{0}, n=0,1,2,3 \ldots D) y_{n}=\left(-0.55 y_{0}\right) ^{n}, n=0,1,2,3 Find the explicit solution of this difference equation in terms of y0 .


A) yn=−0.55ny0,n=0,1,2,3… y_{n}=-0.55 n y_{0}, n=0,1,2,3 \ldots
B) yn=(−0.55) ny0,n=0,1,2,3… y_{n}=(-0.55) ^{n} y_{0}, n=0,1,2,3 \ldots
C) yn=−0.55ny0,n=0,1,2,3… y_{n}=-0.55^{n} y_{0}, n=0,1,2,3 \ldots
D) yn=(−0.55y0) n,n=0,1,2,3 y_{n}=\left(-0.55 y_{0}\right) ^{n}, n=0,1,2,3

E) A) and B)
F) B) and C)

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Solve this initial value problem: Solve this initial value problem: A) 6 x^{2}-x y+8 y^{2}=0 B) 6 x^{2}+x y+8 y^{2}=0 C) 3 x^{2}-x y+4 y^{2}=0 D) 3 x^{2}+x y+4 y^{2}=0


A) 6x2−xy+8y2=0 6 x^{2}-x y+8 y^{2}=0
B) 6x2+xy+8y2=0 6 x^{2}+x y+8 y^{2}=0
C) 3x2−xy+4y2=0 3 x^{2}-x y+4 y^{2}=0
D) 3x2+xy+4y2=0 3 x^{2}+x y+4 y^{2}=0

E) A) and B)
F) A) and C)

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What is the general solution of the differential equation (1 + What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D) ) What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D) = 1 + What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D) ?


A) What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D)
B) What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D)
C) What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D)
D) What is the general solution of the differential equation (1 + ) = 1 + ? A) B) C) D)

E) B) and C)
F) A) and D)

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A city's water reservoir contains 7 billion cubic meters (bcm) of water. The purification system ensures that the concentration of pollutants remains constant at 0.6 kilograms per bcm, and sensors will trigger an alarm if the concentration of pollutants rises above 1 kilogram per bcm. Water flows in and out of the reservoir at the same rate of 0.25 bcm per day, and the concentration of pollutants in the inflow is 2 kilograms per bcm. At all times, the reservoir is well mixed.Set up a differential equation whose solution x(t) is the amount of pollutant in the reservoir at time t. Let t = 0 be the time when the purification system fails. What is x(0)?

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A city's water reservoir contains 6 billion cubic meters (bcm) of water. The purification system ensures that the concentration of pollutants remains constant at 0.5 kilograms per bcm, and sensors will trigger an alarm if the concentration of pollutants rises above 1 kilogram per bcm. Water flows in and out of the reservoir at the same rate of 0.25 bcm per day, and the concentration of pollutants in the inflow is 1.9 kilograms per bcm. At all times, the reservoir is well mixed.If the purification system fails, how much time (in days) elapses before the alarm is triggered? Round your answer to the nearest hundredth of a day.

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What is the general solution of the differential equation What is the general solution of the differential equation A) B) C) D)


A) What is the general solution of the differential equation A) B) C) D)
B) What is the general solution of the differential equation A) B) C) D)
C) What is the general solution of the differential equation A) B) C) D)
D) What is the general solution of the differential equation A) B) C) D)

E) A) and B)
F) C) and D)

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B

Consider the following initial value problem: Consider the following initial value problem: (i) Use Euler's method with two equal steps to find an approximation of y(1). Enter the exact answer, not an approximation. (ii) Solve the initial value problem and compute the solution at x = 1. Enter the exact answer, not an approximation. (iii) What is the error in Euler's method in making this approximation? (i) Use Euler's method with two equal steps to find an approximation of y(1). Enter the exact answer, not an approximation. (ii) Solve the initial value problem and compute the solution at x = 1. Enter the exact answer, not an approximation. (iii) What is the error in Euler's method in making this approximation?

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Consider the autonomous differential equation Consider the autonomous differential equation Determine for the initial condition y(t<sub>0</sub> ) = (8, -4). Determine Consider the autonomous differential equation Determine for the initial condition y(t<sub>0</sub> ) = (8, -4). for the initial condition y(t0 ) = (8, -4).

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Which of these is the general solution of this homogeneous differential equation? Which of these is the general solution of this homogeneous differential equation? A) B) C) D)


A) Which of these is the general solution of this homogeneous differential equation? A) B) C) D)
B) Which of these is the general solution of this homogeneous differential equation? A) B) C) D)
C) Which of these is the general solution of this homogeneous differential equation? A) B) C) D)
D) Which of these is the general solution of this homogeneous differential equation? A) B) C) D)

E) B) and D)
F) B) and C)

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Consider the initial value problem Consider the initial value problem Find all solutions of this initial value problem. Find all solutions of this initial value problem.

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11eeb833_7050_07e3_9020_eb2bf0f290cd_TBW1042_00

What is the general solution of the differential equation What is the general solution of the differential equation A) B) C) D)


A) What is the general solution of the differential equation A) B) C) D)
B) What is the general solution of the differential equation A) B) C) D)
C) What is the general solution of the differential equation A) B) C) D)
D) What is the general solution of the differential equation A) B) C) D)

E) B) and D)
F) All of the above

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Consider the autonomous differential equation Consider the autonomous differential equation Which of these is an equilibrium solution of this differential equation? Select all that apply. A) y = -5 B) y = 5 C) y = 0 D) y = -10 E) y = 10 Which of these is an equilibrium solution of this differential equation? Select all that apply.


A) y = -5
B) y = 5
C) y = 0
D) y = -10
E) y = 10

F) C) and D)
G) A) and D)

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A model of a fishery which grows logistically and is harvested at a constant rate is given by A model of a fishery which grows logistically and is harvested at a constant rate is given by Which of these is an equilibrium solution of this differential equation? Select all that apply. A) y = 0 B) y = -1 C) y = 6 D) y = 1 E) y = -6 Which of these is an equilibrium solution of this differential equation? Select all that apply.


A) y = 0
B) y = -1
C) y = 6
D) y = 1
E) y = -6

F) A) and B)
G) B) and D)

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Consider the differential equation Consider the differential equation Which of these is the general solution to the equation? A) B) C) D) Which of these is the general solution to the equation?


A) Consider the differential equation Which of these is the general solution to the equation? A) B) C) D)
B) Consider the differential equation Which of these is the general solution to the equation? A) B) C) D)
C) Consider the differential equation Which of these is the general solution to the equation? A) B) C) D)
D) Consider the differential equation Which of these is the general solution to the equation? A) B) C) D)

E) C) and D)
F) B) and C)

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What is the solution of this initial value problem? What is the solution of this initial value problem? A) B) C) D)


A) What is the solution of this initial value problem? A) B) C) D)
B) What is the solution of this initial value problem? A) B) C) D)
C) What is the solution of this initial value problem? A) B) C) D)
D) What is the solution of this initial value problem? A) B) C) D)

E) A) and D)
F) A) and C)

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D

Consider the difference equation Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y0 . ?


A) If y0 (\neq\) 0, then the sequence { Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . } diverges to ∞\infty as n →\rightarrow ∞\infty .
B) The sequence { Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . } converges to 6.25 as n →\rightarrow ∞\infty for all values of .
C) If y0 > 0, then the sequence { Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . } converges to 6.25 as n →\rightarrow ∞\infty ; for all other choices of y0 , the sequence { Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . } converges to 0 as n →\rightarrow ∞\infty .
D) D) If y0 ≠\neq 0, then the sequence { Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . } converges to 6.25 as n →\rightarrow ∞\infty ; for all other choices of y0 , the sequence { Consider the difference equation Which of the following is an accurate description of the behavior of the solutions to this difference equation in terms of y<sub>0</sub> . ? A) If y<sub>0</sub> (\neq\) 0, then the sequence { } diverges to \infty as n \rightarrow \infty . B) The sequence { } converges to 6.25 as n \rightarrow \infty for all values of . C) If y<sub>0</sub> > 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . D) D) If y<sub>0</sub> \neq 0, then the sequence { } converges to 6.25 as n \rightarrow \infty ; for all other choices of y<sub>0</sub> , the sequence { } converges to 0 as n \rightarrow \infty . } converges to 0 as n →\rightarrow ∞\infty .

E) B) and D)
F) None of the above

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Identify the integrating factor for this linear differential equation: Identify the integrating factor for this linear differential equation: - 2y = - 2y = Identify the integrating factor for this linear differential equation: - 2y =

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Consider the differential equation Consider the differential equation (i) Which of these is the general solution of this equation? (ii) What choice of the arbitrary constant in the general solution ensures that the solution curve passes through the point (i) Which of these is the general solution of this equation? Consider the differential equation (i) Which of these is the general solution of this equation? (ii) What choice of the arbitrary constant in the general solution ensures that the solution curve passes through the point (ii) What choice of the arbitrary constant in the general solution ensures that the solution curve passes through the point Consider the differential equation (i) Which of these is the general solution of this equation? (ii) What choice of the arbitrary constant in the general solution ensures that the solution curve passes through the point

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Consider the difference equation Consider the difference equation = 0.50 + 6, n = 0, 1, 2, 3...Find the explicit solution of this difference equation in terms of . A) y_{n}=0.50^{n} y_{0}+12, n=0,1,2,3 \ldots B) y_{n}=0.50^{n} y_{0}+4, n=0,1,2,3 \ldots C) y_{n}=0.50^{n-1} y_{0}+6, n=0,1,2,3 \ldots D) y_{n}=0.50^{n-1} y_{0}+12, n=0,1,2,3 \ldots = 0.50 Consider the difference equation = 0.50 + 6, n = 0, 1, 2, 3...Find the explicit solution of this difference equation in terms of . A) y_{n}=0.50^{n} y_{0}+12, n=0,1,2,3 \ldots B) y_{n}=0.50^{n} y_{0}+4, n=0,1,2,3 \ldots C) y_{n}=0.50^{n-1} y_{0}+6, n=0,1,2,3 \ldots D) y_{n}=0.50^{n-1} y_{0}+12, n=0,1,2,3 \ldots + 6, n = 0, 1, 2, 3...Find the explicit solution of this difference equation in terms of Consider the difference equation = 0.50 + 6, n = 0, 1, 2, 3...Find the explicit solution of this difference equation in terms of . A) y_{n}=0.50^{n} y_{0}+12, n=0,1,2,3 \ldots B) y_{n}=0.50^{n} y_{0}+4, n=0,1,2,3 \ldots C) y_{n}=0.50^{n-1} y_{0}+6, n=0,1,2,3 \ldots D) y_{n}=0.50^{n-1} y_{0}+12, n=0,1,2,3 \ldots .


A) yn=0.50ny0+12,n=0,1,2,3… y_{n}=0.50^{n} y_{0}+12, n=0,1,2,3 \ldots
B) yn=0.50ny0+4,n=0,1,2,3… y_{n}=0.50^{n} y_{0}+4, n=0,1,2,3 \ldots
C) yn=0.50n−1y0+6,n=0,1,2,3… y_{n}=0.50^{n-1} y_{0}+6, n=0,1,2,3 \ldots
D) yn=0.50n−1y0+12,n=0,1,2,3… y_{n}=0.50^{n-1} y_{0}+12, n=0,1,2,3 \ldots

E) B) and C)
F) A) and D)

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Consider the differential equation Consider the differential equation Which of the following is the general solution of this equation? A) B) C) D) Which of the following is the general solution of this equation?


A) Consider the differential equation Which of the following is the general solution of this equation? A) B) C) D)
B) Consider the differential equation Which of the following is the general solution of this equation? A) B) C) D)
C) Consider the differential equation Which of the following is the general solution of this equation? A) B) C) D)
D) Consider the differential equation Which of the following is the general solution of this equation? A) B) C) D)

E) None of the above
F) B) and C)

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