1

Which of the following statements about ordinary differential equations is true?

Choose one answer.

a. They may contain one independent variable. | ||

b. They are composed of one or more derivatives with respect to the independent variable. | ||

c. They do not contain partial derivatives. | ||

d. All of the above |

Question
2

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
3

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
4

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
5

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
6

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
7

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
8

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
9

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
10

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
11

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
12

Which of the following relationships is an ordinary differential equation?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
13

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
14

Determine the order of the following differential equation.

Choose one answer.

a. 1 | ||

b. 2 | ||

c. 3 | ||

d. 4 |

Question
15

Which of the following classifications pertain to ordinary differential equations?

Choose one answer.

a. Linear | ||

b. Nonlinear | ||

c. Homogeneous | ||

d. All of the above |

Question
16

Consider the differential equation . Suppose that a
student determined the solution to be . Based upon
this information, is the student correct?

Choose one answer.

a. No, the student should have determined the solution to be . | ||

b. No, the student should have determined the solution to be . | ||

c. No, the student should have determined that there is no solution. | ||

d. Yes, the student did not make any errors. |

Question
17

Apply the superposition principle to find the solution for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
18

Find a particular solution for the following differential equation for which ,

, .

, .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. There is no solution. |

Question
19

Find a particular solution for which passes through
the origin and through the point .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
20

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
21

Find a 1-parameter family of solutions for the following differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. There is no solution. |

Question
22

Find a particular solution for where .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. There is no solution. |

Question
23

The rate at which a radioactive substance decays is proportional to the remaining number of atoms. The differential equation which can be used to describe
this process follows:

represents the number of atoms remaining after seconds. The proportionality constant is considered the decay constant for this process. If represents the number of remaining atoms at seconds, find the general solution.

represents the number of atoms remaining after seconds. The proportionality constant is considered the decay constant for this process. If represents the number of remaining atoms at seconds, find the general solution.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
24

For a circuit containing a capacitor and resistor, the first-order differential equation that describes a discharging capacitor follows:

If represents the charge within the capacitor at seconds, find the general solution. is the capacitance of the capacitor. is the resistance of the resistor.

If represents the charge within the capacitor at seconds, find the general solution. is the capacitance of the capacitor. is the resistance of the resistor.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
25

Earth's atmospheric pressure can be modeled by the
following first-order differential equation.

This differential equation describes the rate at which atmospheric pressure changes with altitude above sea level. is a constant. If represents the atmospheric pressure (millibars) at sea level ( kilometers), find the general solution.

This differential equation describes the rate at which atmospheric pressure changes with altitude above sea level. is a constant. If represents the atmospheric pressure (millibars) at sea level ( kilometers), find the general solution.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
26

Consider where is defined on the interval . It is possible to rewrite this second-order differential equation as a
system of two first-order differential equations using an appropriate change of variable. Using as the new variable, how can be rewritten as a system of two first-order differential equations?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
27

Using Picard's Method of Successive Approximations, attempt to find the first four Picard approximations to the solution for to determine whether or not a solution exists for this first-order
differential equation. It is given that .

Choose one answer.

a. ; the solution exists. | ||

b. ; the solution exists. | ||

c. ; the solution does not exist. | ||

d. ; the solution does not exist. |

Question
28

Construct the direction field for using integer
coordinates from -5 to 5. Analyze the general shape and trajectories. Which of the following represents the equation for a possible integral curve?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. None of the above |

Question
29

Which of the following statements about linear ordinary differential equations is true?

Choose one answer.

a. Linear ordinary differential equations are of the form where and are either constants or functions of . | ||

b. Linear ordinary differential equations are of the form where and are either constants or functions of . | ||

c. Linear ordinary differential equations do not contain partial derivatives. | ||

d. All of the above |

Question
30

Which of the following is a linear ordinary differential equation?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. None of the above |

Question
31

Find the general solution for the following exact differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
32

Find the particular solution for the following separable differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
33

Find the general solution for the following Bernoulli differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
34

Find the particular solution for the following homogeneous differential equation.

where and

where and

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
35

Find the implicit solution to the following differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
36

Solve the following differential equation by separating it:

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
37

Solve the following differential equation by separating it:

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
38

Find the solution for the following differential equation for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
39

Find the solution for the following second-order ordinary differential equation.

where and

where and

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
40

Consider a mass m that oscillates at the end of a spring having a spring constant . The following second-order differential equation describes the vertical
displacement y of this spring-mass system.

This differential equation neglects the influence of air resistance or frictional forces. Find the general solution which describes the vertical displacement of this spring as a function of time .

This differential equation neglects the influence of air resistance or frictional forces. Find the general solution which describes the vertical displacement of this spring as a function of time .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
41

Consider a mass m that oscillates at the end of a spring having a spring constant k. The following second-order differential equation describes the
vertical displacement y of this spring-mass system.

Such a differential equation implies that mass m, once started, will simply oscillate up and down forever! This differential equation neglects the influence of frictional forces. Let us assume that there is a retarding force which is proportional to the velocity of motion where s is treated as a proportionality constant (). The aforementioned differential equation now becomes the following.

Let and where .

There are three possible types of solutions which depend upon the relative size of and , including the following:

Overdamped if ,

Critically damped if ,

Underdamped or oscillatory if .

Find the general solution for this differential equation, which describes the vertical displacement of this spring as a function of time t for "overdamped" motion.

Such a differential equation implies that mass m, once started, will simply oscillate up and down forever! This differential equation neglects the influence of frictional forces. Let us assume that there is a retarding force which is proportional to the velocity of motion where s is treated as a proportionality constant (). The aforementioned differential equation now becomes the following.

Let and where .

There are three possible types of solutions which depend upon the relative size of and , including the following:

Overdamped if ,

Critically damped if ,

Underdamped or oscillatory if .

Find the general solution for this differential equation, which describes the vertical displacement of this spring as a function of time t for "overdamped" motion.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
42

Consider a mass m that oscillates at the end of a spring having a spring constant k. The following second-order differential equation describes the
vertical displacement y of this spring-mass system.

Such a differential equation implies that mass m, once started, will simply oscillate up and down forever! This differential equation neglects the influence of frictional forces. Let us assume that there is a retarding force which is proportional to the velocity of motion where s is treated as a proportionality constant (s > 0). The aforementioned differential equation now becomes the following.

Let and where .

There are three possible types of solutions which depend upon the relative size of and , including the following:

Overdamped if ,

Critically damped if ,

Underdamped or oscillatory if .

Find the general solution for this differential equation, which describes the vertical displacement of this spring as a function of time t for the "critically damped" motion.

Such a differential equation implies that mass m, once started, will simply oscillate up and down forever! This differential equation neglects the influence of frictional forces. Let us assume that there is a retarding force which is proportional to the velocity of motion where s is treated as a proportionality constant (s > 0). The aforementioned differential equation now becomes the following.

Let and where .

There are three possible types of solutions which depend upon the relative size of and , including the following:

Overdamped if ,

Critically damped if ,

Underdamped or oscillatory if .

Find the general solution for this differential equation, which describes the vertical displacement of this spring as a function of time t for the "critically damped" motion.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
43

The one-dimensional time-independent Schrodinger equation is given by the following.

is a wave function which describes the displacement of a single particle of mass where is the total energy, is the potential energy, and is a well-known constant. Since for the particle-in-a-box model where , this second-order differential equation becomes the following.

Find the general solution for this differential equation.

is a wave function which describes the displacement of a single particle of mass where is the total energy, is the potential energy, and is a well-known constant. Since for the particle-in-a-box model where , this second-order differential equation becomes the following.

Find the general solution for this differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
44

Find the general solution for this higher-order differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
45

Find the general solution for this homogeneous ordinary differential equation with constant coefficients (zero right hand side).

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
46

Find the general solution for this ordinary differential equation with constant coefficients (nonzero right hand side).

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
47

Find the general solution for this homogeneous ordinary differential equation with variable coefficients. This is an example of an Euler-Cauchy
differential equation (zero right hand side).

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
48

Find the general solution for this ordinary differential equation with variable coefficients. This is an example of an Euler-Cauchy differential equation
(nonzero right hand side).

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
49

Find the particular solution for the following non-homogeneous ordinary differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
50

Apply the linear differential operator to evaluate
the following expression.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
51

Find the general solution for the following differential equation using the method of undetermined coefficients.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
52

Which of the following expressions is of the correct form to serve as a trial solution for the following differential equation?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
53

Find the general solution for the following differential equation using the method of variation of parameters.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
54

Which of the following statements regarding the method of undetermined coefficients and variation of parameters is true?

Choose one answer.

a. The method of variation of parameters is a much more general method than the method of undetermined coefficients which can be used in many cases. | ||

b. Although the complementary solution is absolutely required when using the method of variation of parameters, it is not required when using the method of undetermined coefficients. | ||

c. When using the method of variation of parameters, it is possible that the acquired integrals cannot be determined. | ||

d. All of the above |

Question
55

Find the general solution for the following ordinary differential equation using a method called the reduction of order.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
56

Given that is a solution of where , it is possible to use a method called reduction of order to find the
general solution of the following ordinary differential equation.

Which of the following expressions would represent within such a determination?

Which of the following expressions would represent within such a determination?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
57

Find the particular solution and complementary
function for the following ordinary differential
equation using the method of inverse operators.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
58

Suppose that you were asked to find the particular solution and complementary function , using the
method of inverse operators, for the following ordinary differential equation.

Identify the inverse operator , which might arise within your solution to this type of problem.

Identify the inverse operator , which might arise within your solution to this type of problem.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
59

Find the power series general solution for the following ordinary differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
60

Which of the following statements are true with regard to a power series solution to the ordinary differential equation ?

Choose one answer.

a. x = 0 and 1 are ordinary points. | ||

b. x = 0 and 1 are regular singularities. | ||

c. x = 0 and 1 are irregular singularities. | ||

d. Insufficient information has been provided to distinguish whether x = 0 and 1 are ordinary points, regular singularities, or irregular singularities. |

Question
61

Find the series solution for an ordinary differential equation using the Frobenius method.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
62

Which of the following statements most accurately describes how the general solution depends upon the order of the Bessel equation shown below?

Choose one answer.

a. In order to satisfy the Bessel equation, the general solution must be , when is a positive non-integer. | ||

b. In order to satisfy the Bessel equation, the general solution must be , when is a positive integer. | ||

c. In order to satisfy the Bessel equation, the general solution must be , when is a positive non-integer. | ||

d. In order to satisfy the Bessel equation, the general solution must be, when is a positive integer. | ||

e. A and B |

Question
63

Which of the following statements most accurately describes how the general solution for the Bessel equation shown below can depend upon a variety of
well-known functions?

Choose one answer.

a. When is a positive non-integer, where and can be expressed in terms of a Gamma function. | ||

b. When is a positive integer, where can be expressed in terms of a Neumann function. | ||

c. When is a positive integer, where can be expressed in terms of and . | ||

d. All of the above |

Question
64

Find the solution for the following differential equation for and .

and

and

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
65

Find the solution for the following differential equation for and .

and

and

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
66

Find the solution for the following differential equation for which and .

and

and

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
67

Find the particular solution for the following non-homogeneous ordinary differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
68

Find the particular solution for the following non-homogeneous ordinary differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
69

Find the solution for the following higher-order differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
70

Find the solution for the following higher-order differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
71

Find the general solution for the following ordinary differential equation using the variation of parameters method.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
72

Find the general solution for the following ordinary differential equation using the method of variation of parameters.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
73

Find the general solution for the following differential equation using the method of variation of parameters.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
74

Find the general solution for the following non-homogeneous ordinary differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
75

Find the general solution for the following non-homogeneous ordinary differential equation.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
76

Find the general solution for the following system of ordinary differential equations.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
77

Suppose that you were given two tanks filled with brine that were connected by pipes. At a rate of 10 gallons per minute, the brine is flowing through the first pipe
from the first tank to the second tank. At the same rate , the brine is flowing through the second pipe from the second tank to the first tank. The initial volume of brine in the first tank is 50 gallons,
and the amount of salt is 15 pounds. The second tank initially contains 25 gallons of pure water. If represents the amount of salt in the first tank and represents the amount of salt in the second tank as a function of
time , which of the following statements is true
regarding the system of ordinary differential equations which model this system?

Choose one answer.

a. | ||

b. | ||

c. pounds, pounds | ||

d. All of the above |

Question
78

Suppose that you were tasked with creating a system of ordinary differential equations to model predator-prey dynamics. Let x and y denote the number of
prey (e.g., rabbits) and predators (e.g., foxes), respectively, as a function of time , where , , , and represent parameters that describe how some predator and prey interact
with each other. Which of the following systems of first-order nonlinear ordinary differential equations describe such a system?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
79

Consider a mass m that oscillates at the end of a spring having a spring constant . The following second-order differential equation describes the vertical
displacement of this spring-mass system.

Such a differential equation implies that mass , once started, will simply oscillate up and down forever! This differential equation neglects the influence of frictional forces. Let us assume that there is a retarding force which is proportional to the velocity of motion where is treated as a proportionality constant (). The aforementioned differential equation now becomes the following.

Let and where .

There are three possible types of solutions which depend upon the relative size of and , including the following:

Overdamped if ,

Critically damped if ,

Underdamped or oscillatory if .

Which of the following differential equations can be used to describe one of these cases?

Such a differential equation implies that mass , once started, will simply oscillate up and down forever! This differential equation neglects the influence of frictional forces. Let us assume that there is a retarding force which is proportional to the velocity of motion where is treated as a proportionality constant (). The aforementioned differential equation now becomes the following.

Let and where .

There are three possible types of solutions which depend upon the relative size of and , including the following:

Overdamped if ,

Critically damped if ,

Underdamped or oscillatory if .

Which of the following differential equations can be used to describe one of these cases?

Choose one answer.

a. | ||

b. | ||

c. | ||

d. Each general solution corresponds to one of the given cases. |

Question
80

Which of the following statements is true regarding the Lotka-Volterra Predator-Prey Model shown below?

Choose one answer.

a. , , , and are positive constants. | ||

b. is the size of the prey population at time . | ||

c. is the size of the predator population at time . | ||

d. All of the above |

Question
81

Which of the following statements is true regarding the differential equations used to describe the double pendulum shown below?

Choose one answer.

a. are all vector quantities. | ||

b. represent mass. | ||

c. represent the length of rigid weightless rods. | ||

d. represent tension. | ||

e. All of the above |

Question
82

Using existence and uniqueness theorems, identify which of the following statements is true regarding the ordinary differential equation , where .

Choose one answer.

a. There exists a solution. | ||

b. The solution exists in some open interval centered at 0. | ||

c. The solution exists and is unique in some (possibly smaller) interval centered at 0. | ||

d. All of the above |

Question
83

It is possible to convert an nth order differential equation into an n-dimensional system of first-order differential equations. For the following
4th-order differential equation, identify the corresponding 4-dimensional system of first-order ordinary differential equations.

Use the following four new variables to make this determination.

Use the following four new variables to make this determination.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
84

There are a variety of methods borrowed from linear algebra that are very useful for finding the solution for systems of linear ordinary differential
equations. One such method includes the usage of matrices. For the following system of linear ordinary differential equations, use these methods to arrive
at the solution in matrix form.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
85

Find the general solution for the following system of ordinary differential equations.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
86

Find the general solution for the following system of ordinary differential equations.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
87

Which of the following statements describe how integral transforms can be used to reduce the complexity of selected classes of mathematics problems?

Choose one answer.

a. An integral transform is an operator (e.g., map one function to another function). | ||

b. The use of selected integral transforms can be used to turn differential equations subject to particular boundary conditions into much simpler algebra problems. | ||

c. The solution that arises as a result of the use of selected integral transforms must be inverted to represent the solution of the original differential equation. | ||

d. All of the above |

Question
88

Using Laplace transforms, find the solution for the following ordinary differential equation.

, where and

Make sure to also identify the specific Laplace transform that was used to arrive at your final solution.

, where and

Make sure to also identify the specific Laplace transform that was used to arrive at your final solution.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
89

Which of the following statements best describes spectra associated with selected Laplace transforms?

Choose one answer.

a. It is possible to use a Laplace transform power spectrum as a basic tool for the complex-exponential decomposition of finite-duration continuous functions. | ||

b. It is possible to use a Laplace transform power spectrum within selected applications which include pole-zero estimation. | ||

c. It is not possible to use a Laplace transform power spectrum as a basic tool for the complex-exponential decomposition of finite-duration continuous functions. | ||

d. A and B are both correct. |

Question
90

Find the inverse Laplace transform for .

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
91

Find the solution for the following initial value problem using Laplace transforms.

, where , and

, where , and

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
92

Using Laplace transforms, find the solution for the following ordinary differential equation.

, where and

Make sure to also identify the specific Laplace transform that was used to arrive at your final solution.

, where and

Make sure to also identify the specific Laplace transform that was used to arrive at your final solution.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
93

Using Laplace transforms, find the solution for the following ordinary differential equation.

, where and

Make sure to also identify the specific Laplace transform that was used to arrive at your final solution.

, where and

Make sure to also identify the specific Laplace transform that was used to arrive at your final solution.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
94

The Verlet Method can be used to approximate the solutions for Newton's Laws of Motion. If r denotes the position of a particle as a function of time with
acceleration a where t represents some small time increment, determine which of the following expressions represents an approximate solution for the
position of this particle.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
95

Predictor-Corrector Methods can be used to approximate the solution for a variety of ordinary differential equations. For the following differential
equation, determine which of the following expressions represents an approximate solution. Let h denote the step size where the trapezoidal rule is
employed.

where

where

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
96

The Runge-Kutta Method can be used to approximate the solution for a variety of ordinary differential equations. For the following differential equation,
determine which of the following expressions represents an approximate solution using the Runge-Kutta 4th Order Method.

where

Let h denote the step size where …

where

Let h denote the step size where …

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
97

The Adam-Bashforth and Adams-Moulton Methods can be used to approximate the solution for a variety of ordinary differential equations. For the following
differential equation, determine an approximate solution for using the 4 Point Adams-Bashforth Method.

where and the step size is 0.1.

where and the step size is 0.1.

Choose one answer.

a. -1.308179 | ||

b. 0.308179 | ||

c. 1.308179 | ||

d. 2.308179 |

Question
98

Find an exact solution for the Lotka-Voltera equations shown below.

Which of the following represent this solution in parametric form?

Which of the following represent this solution in parametric form?

Choose one answer.

a. and where is a constant. | ||

b. and where is a constant. | ||

c. and where is a constant. | ||

d. and where is a constant. |

Question
99

Which of the following statements correctly describes how nonlinear ordinary differential equations can be used to model selected inverted pendulum
dynamics?

Choose one answer.

a. They can be used to model inverted pendulum dynamics involving a stationary pivot point. | ||

b. They can be used to model inverted pendulum dynamics where the inverted pendulum is on a cart consisting of a horizontally moving base. | ||

c. They can be used to model inverted pendulum dynamics where the inverted pendulum is connected to a massless oscillating base. | ||

d. All of the above |

Question
100

Which of the following statements correctly describes how nonlinear ordinary differential equations can be used to model selected double pendulum dynamics?

Choose one answer.

a. They can be used to model double pendulums composed of two simple pendulums. | ||

b. They can be used to model double pendulums composed of two compound pendulums. | ||

c. They can be used to model double pendulums composed of two limbs of equal or unequal lengths and/or masses | ||

d. All of the above |

Question
101

Find the general solution for the Riccati equation shown below.

Choose one answer.

a. | ||

b. | ||

c. | ||

d. |

Question
102

Which of the following statements describe how Nurgaliev's law can be used to model population dynamics?

Choose one answer.

a. The solution for this differential equation can be used to make predictions regarding the size of the population as a function of time which is measured in years. | ||

b. The solution for this differential equation takes into consideration the probability associated with the birth of males or females within a given year. | ||

c. The solution for this differential equation takes into consideration the probability associated with the death of a person within a given year. | ||

d. All of the above |