Filters
Question type
Study Flashcards

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 0.2 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 0.20 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.Set up a differential equation whose solution x(t) is the amount of pollutant in the reservoir at time t and find the particular solution of the differential equation satisfying the initial condition x(0) at time t = 0 when the purification system fails.x(t) = ____________________

Correct Answer

verifed

verified

What is the general solution of the differential equation What is the general solution of the differential equation = y sin x + 6sin x? A) B) C) D) = y sin x + 6sin x?


A) What is the general solution of the differential equation = y sin x + 6sin x? A) B) C) D)
B) What is the general solution of the differential equation = y sin x + 6sin x? A) B) C) D)
C) What is the general solution of the differential equation = y sin x + 6sin x? A) B) C) D)
D) What is the general solution of the differential equation = y sin x + 6sin x? A) B) C) D)

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

Correct Answer

verifed

verified

Identify the integrating factor for this linear differential equation: Identify the integrating factor for this linear differential equation:

Correct Answer

verifed

verified

On another planet, a ball dropped from a height of 5 meters takes 4 seconds to hit the ground.Determine the value of g.

Correct Answer

verifed

verified

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


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

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

Correct Answer

verifed

verified

For what value of K is this differential equation exact? Enter the exact answer, not a decimal approximation. For what value of K is this differential equation exact? Enter the exact answer, not a decimal approximation.

Correct Answer

verifed

verified

The amount of medicine in the bloodstream decays exponentially with a half-life of 5 hours. There must be at least 25 milligrams of medicine per pound of body weight to keep the patient safe during a one-hour procedure.If a patient weighs 130 pounds, how much medicine should be administered at the beginning of the procedure? Round your answer to the nearest milligram.

Correct Answer

verifed

verified

Consider the following initial value problem: Consider the following initial value problem: Determine the first two iterations of Picard's iteration method. Determine the first two iterations of Picard's iteration method. Consider the following initial value problem: Determine the first two iterations of Picard's iteration method.

Correct Answer

verifed

verified

Consider the autonomous differential equation Consider the autonomous differential equation Which of these is a complete list of the equilibrium solutions of this differential equation? A) y=2 k \pi , where k is an integer B) y=0 C) y=k \pi , where k is an integer D) y=\frac{(2 k+1) \pi}{2} , where k is an integer Which of these is a complete list of the equilibrium solutions of this differential equation?


A) y=2kπ y=2 k \pi , where k k is an integer
B) y=0 y=0
C) y=kπ y=k \pi , where k k is an integer
D) y=(2k+1) π2 y=\frac{(2 k+1) \pi}{2} , where k k is an integer

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

Correct Answer

verifed

verified

For what value of K is this differential equation exact? Enter the exact answer, not a decimal approximation For what value of K is this differential equation exact? Enter the exact answer, not a decimal approximation

Correct Answer

verifed

verified

A pie is moved from the oven at 425 degrees Fahrenheit to a freezer at 18 degrees Fahrenheit. After 10 minutes, the pie has cooled to 375 degrees Fahrenheit.Let T(t) be the temperature of the pie t minutes after it has been moved to the freezer. Formulate and solve an initial-value problem for T(t).

Correct Answer

verifed

verified

Consider this initial value problem: Consider this initial value problem: What is approximately the interval where the solution applies? Round each of the endpoints of the interval to the nearest hundredth. What is approximately the interval where the solution applies? Round each of the endpoints of the interval to the nearest hundredth.

Correct Answer

verifed

verified

Which of the following first-order differential equations are exact? Select all that apply.


A) (8y−4x) y′−4y=0 (8 y-4 x) y^{\prime}-4 y=0
B) (2y−5x) +(5y+2x) y′=0 (2 y-5 x) +(5 y+2 x) y^{\prime}=0
C) 4y3+(x4+y4−7x) y′=0 4 y^{3}+\left(x^{4}+y^{4}-7 x\right) y^{\prime}=0
D) (7x−cos⁡(52y) ) −sin⁡(52y) y′=0 \left(7 x-\cos \left(\frac{5}{2} y\right) \right) -\sin \left(\frac{5}{2} y\right) y^{\prime}=0

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

Correct Answer

verifed

verified

Consider the differential equation Consider the differential equation - 3y = . What choice of the arbitrary constant in the general solution ensures that the solution satisfies the initial condition y(0) = 7? - 3y = Consider the differential equation - 3y = . What choice of the arbitrary constant in the general solution ensures that the solution satisfies the initial condition y(0) = 7? . What choice of the arbitrary constant in the general solution ensures that the solution satisfies the initial condition y(0) = 7?

Correct Answer

verifed

verified

The amount of medicine in the bloodstream decays exponentially with a half-life of 7 hours. There must be at least 30 milligrams of medicine per pound of body weight to keep the patient safe during a one-hour procedure. Set up an initial value problem whose solution is the amount of medicine, x(t) (measured in milligrams), in the bloodstream at time t. Let t = 0 correspond to the time when the procedure begins, and assume that x(0) = x0

Correct Answer

verifed

verified

blured image , where k...

View Answer

What is the two-parameter family of solutions of the second-order differential equation What is the two-parameter family of solutions of the second-order differential equation A) y^{2}=C_{1} e^{x}+C_{2} B) \arctan (y) +C_{1}=C_{2} x C) \frac{1}{4} y^{2}+C_{1} \ln |y|=x+C_{2} D) \ln \left|y^{2}+C_{1}\right|=x+C_{2}


A) y2=C1ex+C2 y^{2}=C_{1} e^{x}+C_{2}
B) arctan⁡(y) +C1=C2x \arctan (y) +C_{1}=C_{2} x
C) 14y2+C1ln⁡∣y∣=x+C2 \frac{1}{4} y^{2}+C_{1} \ln |y|=x+C_{2}
D) ln⁡∣y2+C1∣=x+C2 \ln \left|y^{2}+C_{1}\right|=x+C_{2}

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

Correct Answer

verifed

verified

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 For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. For what values of A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. does the fish population become extinct?


A) For all A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. in (0, 1].
B) For all A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. in (0, 1) .
C) For all A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. in (0, 5) .
D) For all A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. in (0, 5].
E) For all A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. in (1, 5) .
F) For all A model of a fishery which grows logistically and is harvested at a constant rate is given by For what values of does the fish population become extinct? A) For all in (0, 1]. B) For all in (0, 1) . C) For all in (0, 5) . D) For all in (0, 5]. E) For all in (1, 5) . F) For all in [1, 5]. in [1, 5].

G) None of the above
H) B) and F)

Correct Answer

verifed

verified

What is the general solution of this first-order differential equation? x What is the general solution of this first-order differential equation? x + 2y = 4 A) B) C) D) + 2y = 4 What is the general solution of this first-order differential equation? x + 2y = 4 A) B) C) D)


A) What is the general solution of this first-order differential equation? x + 2y = 4 A) B) C) D)
B) What is the general solution of this first-order differential equation? x + 2y = 4 A) B) C) D)
C) What is the general solution of this first-order differential equation? x + 2y = 4 A) B) C) D)
D) What is the general solution of this first-order differential equation? x + 2y = 4 A) B) C) D)

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

Correct Answer

verifed

verified

Which of the following first-order differential equations are separable? Select all that apply.


A) Which of the following first-order differential equations are separable? Select all that apply. A) B) C) D) E)
B) Which of the following first-order differential equations are separable? Select all that apply. A) B) C) D) E)
C) Which of the following first-order differential equations are separable? Select all that apply. A) B) C) D) E)
D) Which of the following first-order differential equations are separable? Select all that apply. A) B) C) D) E)
E) Which of the following first-order differential equations are separable? Select all that apply. A) B) C) D) E)

F) A) and D)
G) None of the above

Correct Answer

verifed

verified

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


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

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

Correct Answer

verifed

verified

Showing 21 - 40 of 73

Related Exams

Exam 1

Introduction

28 Questions

Exam 3

Second-Order Linear Differential Equations

119 Questions

Exam 4

Higher-Order Linear Differential Equations

54 Questions

Exam 5

Series Solutions of Second-Order Linear Equations

81 Questions

Exam 6

The Laplace Transform

57 Questions

Exam 7

Systems of First-Order Linear Equations

97 Questions

Exam 8

Numerical Methods

63 Questions

Exam 9

Nonlinear Differential Equations and Stability

76 Questions

Exam 10

Partial Differential Equations and Fourier Series

44 Questions

Exam 11

Boundary Value Problems and Sturm-Liouville Theory

19 Questions

Show Answer