Question 1

​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 2

​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 3

​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 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

​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 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content.After 1 hour,the towel has lost 40% of its original moisture content.How long will it take the towel to lose 80% of its original moisture content? ​

Accepted Answer

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

Question 13

​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 14

Find the particular solution of the differential equation   that satisfies the initial condition   when   ,where   is the general solution. ​

Accepted Answer

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

Question 15

​A medical researcher wants to determine the concentration C (in moles per liter)of a tracer drug injected into a moving fluid with flow R (in liters per minute).Solve this problem by considering a single-compartment dilution model (see figure).Assume that the fluid is continuously mixed and that the volume V (in liters)of fluid in the compartment is constant. ​   ​
If the tracer is injected instantaneously at time   ,then the concentration of the fluid in the compartment begins diluting according to the differential equation   ,   when   (a)Solve this differential equation to find the concentration as a function of time.
(b)Find the limit of ​C as   ​​

Accepted Answer

A)  ​a.  
​b) 1
​ 
B)  ​a.  
​b) 0
​​ 
C)  ​a.  
​b) 2
​​ 
D)  ​a.  
​b) 0
​​ 
E)  ​​a.  
​b)1
​​​ 
A)  ​a.  
​b) 1
​ 
B)  ​a.  
​b) 0
​​ 
C)  ​a.  
​b) 2
​​ 
D)  ​a.  
​b) 0
​​ 
E)  ​​a.  
​b)1
​​​

Question 16

​Write the the differential equation by separating the variables. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​No, the variables cannot be separated 
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​No, the variables cannot be separated 
E)  ​

Question 17

Use this equation   and find ​P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously. ​​

Accepted Answer

A)  ​$110,708,538.49​ 
B)  $10,500,538.49 
C)  $10,708,538.49 
D)  $100,708,538.49 
E)  $1,708,538.49 
A)  ​$110,708,538.49​ 
B)  $10,500,538.49 
C)  $10,708,538.49 
D)  $100,708,538.49 
E)  $1,708,538.49

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

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

Determine whether the function is a solution of the differential equation

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

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

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

Use integration to find a general solution of the differential equation

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

Determine whether the function is a solution of the differential equation

A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content.After 1 hour,the towel has lost 40% of its original moisture content.How long will it take the towel to lose 80% of its original moisture content?

Determine whether is a solution of the differential equation

Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution.

Write the the differential equation by separating the variables.

Use this equation and find P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously.

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

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

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

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

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

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

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

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

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

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

A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content.After 1 hour,the towel has lost 40% of its original moisture content.How long will it take the towel to lose 80% of its original moisture content? ​

​Determine whether is a solution of the differential equation ​

Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​

​Write the the differential equation by separating the variables. ​ ​

Use this equation and find ​P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously. ​​

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

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

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

Determine whether the function is a solution of the differential equation

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

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

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

Use integration to find a general solution of the differential equation

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

Determine whether the function is a solution of the differential equation

A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content.After 1 hour,the towel has lost 40% of its original moisture content.How long will it take the towel to lose 80% of its original moisture content?

Determine whether is a solution of the differential equation

Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution.

Write the the differential equation by separating the variables.

Use this equation and find P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously.