Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134668574
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 9.1, Problem 23E
In Problems 21–24, determine which of the slope fields (A)–(D) is associated with the indicated differential equation. Briefly justify your answer.
23. xy′ = –y (From Problem 13)
13.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
4. What is the differential equation of the given functions?
• y = Ce-* + Cze-2x +x
y = Ce2* + C2e-*
23. By suitably renaming the constants and dependent variables in the equations
and
T'=k(T-Tm)
G' = -XG+r
discussed in Section 1.2 in connection with Newton's law of cooling and absorption of glucose in the body, we can write both as
y' = -ay+b,
(A)
(B)
(C)
where a is a positive constant and b is an arbitrary constant. Thus, (A) is of the form (C) with y = T, a = k, and b = kT, and (B) is of the form (C) with y = G,
a = λ, and b = r. We'll encounter equations of the form (C) in many other applications in Chapter 2.
Choose a positive a and an arbitrary b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form
{0≤t≤T, c≤y≤d}
of the ty-plane. Vary T, c, and d until you discover a common property of all the solutions of (C). Repeat this experiment with various choices of a and b until you
can state this property precisely in terms of a and b.
3. The differential equation of the family of curves whose equation is y = x' + ax? +bx+5
given by Ay"+By'+Cy Dx'+10. Find A, B, C, and D. The letters A to D can contain
is
numbers, variables, or combination thereof.
Chapter 9 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MPCh. 9.1 - Prob. 3MPCh. 9.1 - Prob. 4MPCh. 9.1 - Prob. 5MPCh. 9.1 - Prob. 1EDCh. 9.1 - Prob. 2EDCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3E
Ch. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - In Problems 110, find the derivative. (If...Ch. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.1 - In Problems 1120, show that the given function is...Ch. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - In Problems 2124, determine which of the slope...Ch. 9.1 - In Problems 2124, determine which of the slope...Ch. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - In Problems 2528, use the appropriate slope...Ch. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - In Problems 2938, show that the given function y...Ch. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - In Problems 2938, show that the given function y...Ch. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - If y is defined implicitly by the given equation,...Ch. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - In Problems 55 and 56, use the general solution y...Ch. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - In Problems 59 and 60, use window dimensions Xmin...Ch. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Rumor spreadGompertz growth model. The rate of...Ch. 9.2 - Solve: y=4x3y2.Ch. 9.2 - Prob. 2MPCh. 9.2 - Repeat Example 3 if the mothballs lose half their...Ch. 9.2 - Prob. 4MPCh. 9.2 - Prob. 5MPCh. 9.2 - Prob. 1EDCh. 9.2 - Prob. 2EDCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - In Problems 18, find the most general...Ch. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - In Problems 912, write a differential equation...Ch. 9.2 - In Problems 912, write a differential equation...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - In Problems 3140, find the general solution for...Ch. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - In Problems 3140, find the general solution for...Ch. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - In Problems 4146, find the general solution for...Ch. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 56ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - Prob. 60ECh. 9.2 - Advertising. A company is using radio advertising...Ch. 9.2 - Prob. 62ECh. 9.2 - Prob. 63ECh. 9.2 - Prob. 64ECh. 9.2 - Prob. 65ECh. 9.2 - Prob. 66ECh. 9.2 - Prob. 67ECh. 9.2 - Prob. 68ECh. 9.2 - Prob. 69ECh. 9.2 - Prob. 70ECh. 9.2 - Prob. 71ECh. 9.2 - Prob. 72ECh. 9.2 - Newtons law of cooling states that the rate of...Ch. 9.2 - Prob. 74ECh. 9.2 - Population growth. A culture of bacteria is...Ch. 9.2 - Prob. 76ECh. 9.2 - Prob. 77ECh. 9.2 - Prob. 78ECh. 9.2 - Prob. 79ECh. 9.2 - Prob. 80ECh. 9.2 - Prob. 81ECh. 9.2 - Learning. The number of words per minute. N, a...Ch. 9.2 - Prob. 83ECh. 9.3 - Solve:xy+3y=4x.Ch. 9.3 - Prob. 2MPCh. 9.3 - Repeat Example 3 if the account earns 5%...Ch. 9.3 - If D = 70 + 2p(t) + 2p(t), S = 30 + 6p(t) + 3p(t)....Ch. 9.3 - Repeat Example 5 if water is released from the...Ch. 9.3 - Prob. 1EDCh. 9.3 - Prob. 2EDCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 25ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - In Problems 3514, find the integrating factor fix...Ch. 9.3 - In Problems 3514, find the integrating factor fix...Ch. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Prob. 57ECh. 9.3 - Prob. 58ECh. 9.3 - Prob. 59ECh. 9.3 - Prob. 60ECh. 9.3 - Prob. 61ECh. 9.3 - Prob. 62ECh. 9.3 - Prob. 63ECh. 9.3 - Prob. 64ECh. 9.3 - Prob. 65ECh. 9.3 - Prob. 66ECh. 9.3 - Supply-demand. The supply S and demand D for a...Ch. 9.3 - Prob. 68ECh. 9.3 - Pollution. A 1,000-gallon holding tank contains...Ch. 9.3 - Pollution. Rework Problem 69 if water is entering...Ch. 9.3 - Pollution. Rework Problem 69 if water is entering...Ch. 9.3 - Prob. 72ECh. 9.3 - Pollution. Refer to Problem 69. When will the tank...Ch. 9.3 - Prob. 74ECh. 9.3 - Prob. 75ECh. 9.3 - Prob. 76ECh. 9.3 - Prob. 77ECh. 9.3 - In an article in the College Mathematics Journal...Ch. 9.3 - Prob. 79ECh. 9.3 - In 1960, William K. Estes proposed the following...Ch. 9 - In Problems 1 and 2, show that the given function...Ch. 9 - In Problems 1 and 2, show that the given function...Ch. 9 - In Problems 3 and 4, determine which of the...Ch. 9 - In Problems 3 and 4, determine which of the...Ch. 9 - In Problems 5 and 6, use the appropriate slope...Ch. 9 - In Problems 5 and 6, use the appropriate slope...Ch. 9 - In Problems 7 and 8, write a differential equation...Ch. 9 - In Problems 7 and 8, write a differential equation...Ch. 9 - In Problems 9 and 10, describe in words the rate...Ch. 9 - In Problems 9 and 10, describe in words the rate...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - Prob. 16RECh. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - Prob. 23RECh. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - Solve the following differential equation two...Ch. 9 - Give an example of an equation that can be solved...Ch. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Rumor spread. A single individual starts a rumor...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- For each dif erential equation in Problems 1–21, find the general solutionby finding the homogeneous solution and a particular solution. Please DO NOT YOU THE PI method where 1/f(r) * x. Dont do that. Instead do this, assume for yp = to something, do the 1 and 2 derivative of it and then plug it in the equation to find the answer.arrow_forward2. A differential equation that is a function of x only will produce a slope field with parallel tangents along the diagonal will produce a slope field that does not have rows or columns of parallel tangents will produce a slope field with rows of parallel tangents O will produce a slope field with columns of parallel tangentsarrow_forward#10 onlyarrow_forward
- 8. The differential equation modeling population growth while incorporating the carrying capacity is = rN (1 -). dt Suppose that the population of deer has a growth rate of 0.1 per year and an environmental limitation of 4600 deer. If there are currently 1700 deer, how many deer will there be in five years?arrow_forward5. A population of butterflies is released into a den and is growing according to the logistic equation. Suppose that the carrying capacity is 800 butterflies with a relative growth rate of k = 0.2 per month. Write the differential equation describing the logistic population model for this problem.arrow_forward3.1 Draw the phase plane diagram for the differential equation x" = -x + x³. What is the equation of the separatrix for this problem?arrow_forward
- Problem 19. Consider the differential equation y =f(x), where the graph of the function f is shown below. Use this graph to construct a slope field for this differential equation, then use your slope field to approximate the graph of the solution which passes through the point (-1,1) and the solution which passes through the point -4,-1). y -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0,5 X -2 -4 -6 -8arrow_forward1. Consider a boat in the ocean, which is carrying contraband. Near to this boat is a lighthouse on a small island, which is attempting to track this boat with its searchlight. This ray of light originates at the lighthouse, and passes through the boat's position precisely at all times. The boat tries to escape the lighthouses' tracking by moving at a constant angle relative to the ray of light. (a) Write a differential equation which π ocean. You may assume that 0 = or 2' 2 Hint: It may be helpful to consider the angle a(t) between the lighthouse and the boat at time t. models the boat's path through the 3π ㅠ 4' = (b) Suppose and is first discovered at the position 3 kilometres east, and 4 kilometres to the north of the lighthouse. Solve for the curve that the boat travels along. Write your answer in polar coordinates. ㅠ (c) Sketch the direction field of the ODE if curves, i.e solution curves, in this case? = 2 What are the integral (d) With with arbitrary consider the direction…arrow_forwardPLEASE ANSWER ASAParrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY