Question 1

Solve the differential equation.

Accepted Answer

The answer of Solve the differential equation.  ...

Question 2

Which equation does the function   satisfy?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
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E)

Question 3

Which of the following functions are the constant solutions of the equation   
a.   
b.   
c.   
d.   
e.

Accepted Answer

The answer of Which of the following functions are the...

Question 4

Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?

Accepted Answer

The answer of Let c be a positive number. A...

Question 5

Solve the differential equation.

Accepted Answer

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B)    
C)    
D)    
E)    
A)    
B)    
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D)    
E)

Question 6

Kirchhoff's Law gives us the derivative equation   .
If   , use Euler's method with step size 0.1 to estimate   after 0.3 second.

Accepted Answer

The answer of Kirchhoff's Law gives us the derivative equation...

Question 7

The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. Use the logistic model to predict the world population in the 2,450 year. Calculate your answer in billions to one decimal place. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate.)

Accepted Answer

A) 59.2 billion 
B) 32.9 billion 
C) 78.3 billion 
D) 17.1 billion 
E) 24.1 billion 
A) 59.2 billion 
B) 32.9 billion 
C) 78.3 billion 
D) 17.1 billion 
E) 24.1 billion

Question 8

Solve the initial-value problem.

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Question 9

Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.

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Question 10

An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   .
Find the limiting velocity.

Accepted Answer

The answer of An object with mass m is dropped...

Question 11

The solution of the differential equation   satisfies the initial condition   .
Find the limit.

Accepted Answer

The answer of The solution of the differential equation ...

Question 12

In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.

Accepted Answer

A)  0.75 A 
B)    
C)    
D)    
E)    
A)  0.75 A 
B)    
C)    
D)    
E)

Question 13

Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.

Accepted Answer

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B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Select a direction field for the differential equation   from a set of direction fields labeled I-IV.

Accepted Answer

The answer of Select a direction field for the differential...

Question 15

Solve the differential equation.

Accepted Answer

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B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Solve the differential equation.

Accepted Answer

The answer of Solve the differential equation.  ...

Question 19

Solve the differential equation.

Accepted Answer

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B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Solve the initial-value problem.

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Solve the differential equation.

Which equation does the function satisfy?

Which of the following functions are the constant solutions of the equation a. b. c. d. e.

Solve the differential equation.

Kirchhoff's Law gives us the derivative equation . If , use Euler's method with step size 0.1 to estimate after 0.3 second.

Solve the initial-value problem.

Suppose that a population grows according to a logistic model with carrying capacity and per year. Choose the logistic differential equation for these data.

The solution of the differential equation satisfies the initial condition . Find the limit.

In the circuit shown in Figure, a generator supplies a voltage of volts, the inductance is 2 H, the resistance is 40 , and . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.

Let be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.

Select a direction field for the differential equation from a set of direction fields labeled I-IV.

Solve the differential equation.

We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ,

Solve the differential equation.

Solve the differential equation.

Solve the initial-value problem.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 9: Differential Equations

Solve the differential equation.

Which equation does the function satisfy?

Which of the following functions are the constant solutions of the equation a. b. c. d. e.

Solve the differential equation.

Kirchhoff's Law gives us the derivative equation . If , use Euler's method with step size 0.1 to estimate after 0.3 second.

Solve the initial-value problem.

Suppose that a population grows according to a logistic model with carrying capacity and per year. Choose the logistic differential equation for these data.

The solution of the differential equation satisfies the initial condition . Find the limit.

In the circuit shown in Figure, a generator supplies a voltage of volts, the inductance is 2 H, the resistance is 40 , and . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.

Let be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.

Select a direction field for the differential equation from a set of direction fields labeled I-IV.

Solve the differential equation.

We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ,

Solve the differential equation.

Solve the differential equation.

Solve the initial-value problem.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters