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

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

​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 4

Use the Gompertz growth model described to find the population y as a function of time ​t (in years). ​   when   ;   when   ​   ​

Accepted Answer

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

Question 5

​Find the general solution of the first-order linear differential equation. ​
​   ​

Accepted Answer

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

Question 6

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 7

​Use this equation   and find ​A for each situation. 
(a)   ,   and   years
(b)   ,   and   years
​​

Accepted Answer

A)  ​a) 685,099.00
​b) 5,802,815.12
​ 
B)  ​a) 585,099.00
​b) 5,802,815.12
​​ 
C)  ​a) 685,099.00
​b) 6,802,815.12
​​ 
D)  ​a) 585,099.00
​b) 4,802,815.12
​​ 
E)  ​
​a)485,099.00
​b)5,802,815.12
​
​​ 
A)  ​a) 685,099.00
​b) 5,802,815.12
​ 
B)  ​a) 585,099.00
​b) 5,802,815.12
​​ 
C)  ​a) 685,099.00
​b) 6,802,815.12
​​ 
D)  ​a) 585,099.00
​b) 4,802,815.12
​​ 
E)  ​
​a)485,099.00
​b)5,802,815.12
​
​​

Question 8

​Determine whether   is a solution of the differential equation   ​

Accepted Answer

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

Question 9

​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 10

Assume that the rate of change in y is proportional to ​y.Solve the resulting differential equation   and find the particular solution that passes through the points   ,   ​

Accepted Answer

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

Question 11

Use the hybrid selection model described to find the percent y (in decimal form)of the population that has the indicated characteristics as a function of time ​t (in generations). ​   when   ;   when   ​   ​

Accepted Answer

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

Question 12

​Find the general solution of the first-order linear differential equation. ​
​   ​

Accepted Answer

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

Question 13

​Find the general solution of the first-order linear differential equation. ​
​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

​Solve for ​y in two ways. ​
​   ​

Accepted Answer

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

Question 17

​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 18

​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 19

The isotope   has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places. ​

Accepted Answer

A)  4.7495 g, 0.0137 g 
B)  2.714 g, 0.0078 g 
C)  6.785 g, 0.0195 g 
D)  8.142 g, 0.0234 g 
E)  4.071 g,0.0273 g 
A)  4.7495 g, 0.0137 g 
B)  2.714 g, 0.0078 g 
C)  6.785 g, 0.0195 g 
D)  8.142 g, 0.0234 g 
E)  4.071 g,0.0273 g

Question 20

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

Accepted Answer

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

Use separation of variables to find the 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

Use the Gompertz growth model described to find the population y as a function of time t (in years). when ; when

Find the general solution of the first-order linear differential equation.

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

Use this equation and find A for each situation. (a) , and years (b) , and years

Determine whether is a solution of the differential equation

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

Assume that the rate of change in y is proportional to y.Solve the resulting differential equation and find the particular solution that passes through the points ,

Use the hybrid selection model described to find the percent y (in decimal form)of the population that has the indicated characteristics as a function of time t (in generations). when ; when

Find the general solution of the first-order linear differential equation.

Find the general solution of the first-order linear differential equation.

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

Write the the differential equation by separating the variables.

Solve for y in two ways.

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.

Determine whether is a solution of the differential equation

The isotope has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places.

Write the the differential equation by separating the variables.

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. ​ ​

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

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

Use the Gompertz growth model described to find the population y as a function of time ​t (in years). ​ when ; when ​ ​

​Find the general solution of the first-order linear differential equation. ​ ​ ​

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

​Use this equation and find ​A for each situation. (a) , and years (b) , and years ​​

​Determine whether is a solution of the differential equation ​

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

Assume that the rate of change in y is proportional to ​y.Solve the resulting differential equation and find the particular solution that passes through the points , ​

Use the hybrid selection model described to find the percent y (in decimal form)of the population that has the indicated characteristics as a function of time ​t (in generations). ​ when ; when ​ ​

​Find the general solution of the first-order linear differential equation. ​ ​ ​

​Find the general solution of the first-order linear differential equation. ​ ​ ​

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

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

​Solve for ​y in two ways. ​ ​ ​

​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. ​ ​ ​

​Determine whether is a solution of the differential equation ​

The isotope has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places. ​

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

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.

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

Determine whether the function is a solution of the differential equation

Use the Gompertz growth model described to find the population y as a function of time t (in years). when ; when

Find the general solution of the first-order linear differential equation.

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

Use this equation and find A for each situation. (a) , and years (b) , and years

Determine whether is a solution of the differential equation

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

Assume that the rate of change in y is proportional to y.Solve the resulting differential equation and find the particular solution that passes through the points ,

Use the hybrid selection model described to find the percent y (in decimal form)of the population that has the indicated characteristics as a function of time t (in generations). when ; when

Find the general solution of the first-order linear differential equation.

Find the general solution of the first-order linear differential equation.

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

Write the the differential equation by separating the variables.

Solve for y in two ways.

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.

Determine whether is a solution of the differential equation

The isotope has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places.

Write the the differential equation by separating the variables.