Question 1

​Write the first-order linear differential equation in standard form. ​
​   ​

Accepted Answer

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

Question 2

Find the particular solution that satisfies the initial condition.   ; Initial Condition:   when   ​

Accepted Answer

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

Question 3

Some of the curves corresponding to different values of C in general solution of the differential equation   ,   are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph. ​   ​

Accepted Answer

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

Question 4

​Use separation of variables to find the general solution of the differential equation. ​   ​

Accepted Answer

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

Question 5

​Use the initial condition to find the particular solution of the differential equation. ​   ,   when   ​

Accepted Answer

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

Question 6

​Use the integration to find the general solution of the differential equation   ​

Accepted Answer

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

Question 7

​Determine whether   is a solution of the differential equation   ​

Accepted Answer

A)  ​   and   
B)  ​​   and   
C)  ​​   and   
D)  ​​   and   
E)  ​​   and   
A)  ​   and   
B)  ​​   and   
C)  ​​   and   
D)  ​​   and   
E)  ​​   and

Question 8

​Use separation of variables to find the general solution of the differential equation. ​   ​

Accepted Answer

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

Question 9

​Use integration to find a general solution of the differential equation. ​
​   ​

Accepted Answer

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

Question 10

Find the particular solution of the differential equation   passing through the point   ​

Accepted Answer

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

Question 11

Which of the following is a solution of the differential equation   ? ​

Accepted Answer

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

Question 12

​Determine whether the function   is a solution of the differential equation   ​

Accepted Answer

A)  Solution 
B)  ​Not a solution 
A)  Solution 
B)  ​Not a solution

Question 13

Use the integration to find the general solution of the differential equation   ​

Accepted Answer

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

Question 14

Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition. ​

Accepted Answer

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

Question 15

The rate of change in sales S (in thousands of units)of a new product is proportional to the difference between L and S at any time t (in years),where ​L is the maximum number of units of the new product available.When   ,   Write and solve the differential equation for this sales model. ​

Accepted Answer

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

Question 16

​Use separation of variables to find the general solution of the differential equation. ​   ​

Accepted Answer

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

Question 17

A population of eight beavers has been introduced into a new wetlands area.Biologists estimate that the maximum population the wetlands can sustain is 60 beavers.After 3 years,the population is 15 beavers.The population follows a Gompertz growth model.How many beavers will there be in the wetlands after 10 years? ​

Accepted Answer

A)  34 beavers 
B)  32 beavers 
C)  30 beavers 
D)  31 beavers 
E)  39 beavers 
A)  34 beavers 
B)  32 beavers 
C)  30 beavers 
D)  31 beavers 
E)  39 beavers

Question 18

Find the particular solution of the differential equation   that satisfies the boundary condition   ​

Accepted Answer

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

Question 19

A calf that weighs 75 pounds at birth gains weight at the rate   ,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for   ​

Accepted Answer

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

Question 20

​Solve the differential equation to find velocity v as a function of time ​t if   when   The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance. ​   ​

Accepted Answer

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

Write the first-order linear differential equation in standard form.

Find the particular solution that satisfies the initial condition. ; Initial Condition: when

Some of the curves corresponding to different values of C in general solution of the differential equation , are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.

Use separation of variables to find the general solution of the differential equation.

Use the initial condition to find the particular solution of the differential equation. , when

Use the integration to find the general solution of the differential equation

Determine whether is a solution of the differential equation

Use separation of variables to find the general solution of the differential equation.

Use integration to find a general solution of the differential equation.

Find the particular solution of the differential equation passing through the point

Which of the following is a solution of the differential equation ?

Determine whether the function is a solution of the differential equation

Use the integration to find the general solution of the differential equation

Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition.

The rate of change in sales S (in thousands of units)of a new product is proportional to the difference between L and S at any time t (in years),where L is the maximum number of units of the new product available.When , Write and solve the differential equation for this sales model.

Use separation of variables to find the general solution of the differential equation.

Find the particular solution of the differential equation that satisfies the boundary condition

A calf that weighs 75 pounds at birth gains weight at the rate ,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for

Solve the differential equation to find velocity v as a function of time t if when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Filters

Exam 11: Differential Equations

​Write the first-order linear differential equation in standard form. ​ ​ ​

Find the particular solution that satisfies the initial condition. ; Initial Condition: when ​

Some of the curves corresponding to different values of C in general solution of the differential equation , are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph. ​ ​

​Use separation of variables to find the general solution of the differential equation. ​ ​

​Use the initial condition to find the particular solution of the differential equation. ​ , when ​

​Use the integration to find the general solution of the differential equation ​

​Determine whether is a solution of the differential equation ​

​Use separation of variables to find the general solution of the differential equation. ​ ​

​Use integration to find a general solution of the differential equation. ​ ​ ​

Find the particular solution of the differential equation passing through the point ​

Which of the following is a solution of the differential equation ? ​

​Determine whether the function is a solution of the differential equation ​

Use the integration to find the general solution of the differential equation ​

Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition. ​

The rate of change in sales S (in thousands of units)of a new product is proportional to the difference between L and S at any time t (in years),where ​L is the maximum number of units of the new product available.When , Write and solve the differential equation for this sales model. ​

​Use separation of variables to find the general solution of the differential equation. ​ ​

Find the particular solution of the differential equation that satisfies the boundary condition ​

A calf that weighs 75 pounds at birth gains weight at the rate ,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for ​

​Solve the differential equation to find velocity v as a function of time ​t if when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance. ​ ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Filters

Write the first-order linear differential equation in standard form.

Find the particular solution that satisfies the initial condition. ; Initial Condition: when

Some of the curves corresponding to different values of C in general solution of the differential equation , are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.

Use separation of variables to find the general solution of the differential equation.

Use the initial condition to find the particular solution of the differential equation. , when

Use the integration to find the general solution of the differential equation

Determine whether is a solution of the differential equation

Use separation of variables to find the general solution of the differential equation.

Use integration to find a general solution of the differential equation.

Find the particular solution of the differential equation passing through the point

Which of the following is a solution of the differential equation ?

Determine whether the function is a solution of the differential equation

Use the integration to find the general solution of the differential equation

Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition.

The rate of change in sales S (in thousands of units)of a new product is proportional to the difference between L and S at any time t (in years),where L is the maximum number of units of the new product available.When , Write and solve the differential equation for this sales model.

Use separation of variables to find the general solution of the differential equation.

Find the particular solution of the differential equation that satisfies the boundary condition

A calf that weighs 75 pounds at birth gains weight at the rate ,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for

Solve the differential equation to find velocity v as a function of time t if when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance.