Differential Equations
4th Edition
ISBN: 9780495561989
Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1.1, Problem 4E
Consider the population model
where P(t) is the population at time t.
(a) For what values of P is the population in equilibrium?
(b) For what values of P is the population increasing?
(c) For what values of P is the population decreasing?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)
Q1:
A slider in a machine moves along a fixed straight rod. Its
distance x cm along the rod is given below for various values of the time. Find the
velocity and acceleration of the slider when t = 0.3 seconds.
t(seconds)
x(cm)
0 0.1 0.2 0.3 0.4 0.5 0.6
30.13 31.62 32.87 33.64 33.95 33.81 33.24
Q2:
Using the Runge-Kutta method of fourth order, solve for y atr = 1.2,
From
dy_2xy +et
=
dx x²+xc*
Take h=0.2.
given x = 1, y = 0
Q3:Approximate the solution of the following equation
using finite difference method.
ly -(1-y=
y = x), y(1) = 2 and y(3) = −1
On the interval (1≤x≤3).(taking h=0.5).
Ф
sketch stability
x= -4x + 2xy - 8
y° =
4 y 2 - x²
чуг.
Chapter 1 Solutions
Differential Equations
Ch. 1.1 - In Exercises 1 and 2, find the equilibrium...Ch. 1.1 - In Exercises 1 and 2, find the equilibrium...Ch. 1.1 - Consider the population model dPdt=0.4P(1P230)...Ch. 1.1 - Consider the population model ...Ch. 1.1 - Consider the differential equation dydt=y3y212y...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...
Ch. 1.1 - MacQuarie Island is a small island about half-way...Ch. 1.1 - The velocity u of a freefalling skydiver is well...Ch. 1.1 - Exercises 13—15 consider an elementary model of...Ch. 1.1 - Exercises 13—15 consider an elementary model of...Ch. 1.1 - Exercises 13—15 consider an elementary model of...Ch. 1.1 - The expenditure on education in the U.S. is given...Ch. 1.1 - Suppose a species of fish in a particular lake has...Ch. 1.1 - Suppose that the growth-rate parameter k = 0.3 and...Ch. 1.1 - The rhinoceros is now extremely rare. Suppose...Ch. 1.1 - While it is difficult to imagine a time before...Ch. 1.1 - For the following predator-prey systems, identify...Ch. 1.1 - In the following predator-prey population models,x...Ch. 1.1 - The following systems are models of the...Ch. 1.2 - Bob. Glen. and Paul are once again sitting around...Ch. 1.2 - Make up a differential equation of the form ...Ch. 1.2 - Make up a differential equation of the form dy/dt...Ch. 1.2 - In Section 1.1, we guessed solutions to the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - Prob. 38ECh. 1.2 - A 5-gallon bucket is full of pure water. Suppose...Ch. 1.2 - Consider the following very simple model of blood...Ch. 1.2 - A cup of hot chocolate is initially 170o Fand is...Ch. 1.2 - Suppose you are having a dinner party for a large...Ch. 1.2 - Prob. 43ECh. 1.3 - In Exercises 1-6, sketch the slope fields for the...Ch. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - In Exercises 710, a differential equation and its...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Suppose we know that the function f(t, y) is...Ch. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Consider the autonomous differential equation ...Ch. 1.3 - Eight differential equations and four slope fields...Ch. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.4 - In Exercises 14, use EulersMethod to perform...Ch. 1.4 - In Exercises 14, use EulersMethod to perform...Ch. 1.4 - Prob. 3ECh. 1.4 - In Exercises 14, use EulersMethod to perform...Ch. 1.4 - In Exercises 510, use Euler’s method with the...Ch. 1.4 - In Exercises 510, use Euler’s method with the...Ch. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Consider the initial-value problem dy/dt= y ,y(0)...Ch. 1.4 - Consider the initial-value problem dy/dt= 2 ...Ch. 1.4 - As we saw in Exercise 19 of Section 1.3, the...Ch. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.5 - In Exercises 1—4, we refer to a function f, but we...Ch. 1.5 - Prob. 2ECh. 1.5 - In Exercises 1—4, we refer to a function f, but we...Ch. 1.5 - In Exercises 1—4, we refer to a function f, but we...Ch. 1.5 - Prob. 5ECh. 1.5 - In Exercises 5—8, an initial condition for the...Ch. 1.5 - Prob. 7ECh. 1.5 - In Exercises 5—8, an initial condition for the...Ch. 1.5 - (a) Show that y1(t)=t2 and y2(t)=t2+1 are...Ch. 1.5 - Consider the differential equation dy/dt=2y (a)...Ch. 1.5 - Consider the differential equation dydt=yt2 (a)...Ch. 1.5 - (a) Show that y1(t)=1t1 and y2(t)=1t2 are...Ch. 1.5 - Prob. 13ECh. 1.5 - In Exercises 13—16, an initial-value problem is...Ch. 1.5 - In Exercises 13—16, an initial-value problem is...Ch. 1.5 - In Exercises 13—16, an initial-value problem is...Ch. 1.5 - Prob. 17ECh. 1.5 - We have emphasized that the Uniqueness Theorem...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 3ECh. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 5ECh. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 9ECh. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - Prob. 16ECh. 1.6 - ]In Exercises 1321, a differential equation and...Ch. 1.6 - Prob. 18ECh. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - Prob. 23ECh. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - Prob. 27ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - In Exercises 2932, the graph of a function f(y) is...Ch. 1.6 - In Exercises 2932, the graph of a function f(y) is...Ch. 1.6 - In Exercises 2932, the graph of a function f(y) is...Ch. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Eight differential equations and four phase lines...Ch. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Consider the Ermentrout-Kopell model for the...Ch. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Let x(t) be the amount of time between two...Ch. 1.6 - Prob. 46ECh. 1.6 - Use the model in Exercise 45 to predict what...Ch. 1.6 - Prob. 48ECh. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Prob. 9ECh. 1.7 - Prob. 10ECh. 1.7 - The graph to the right is the graph of a function...Ch. 1.7 - The graph to the right is the graph of a function...Ch. 1.7 - Six one-parameter families of different equations...Ch. 1.7 - Consider the Ermentrout-Kopell model for the...Ch. 1.7 - Prob. 15ECh. 1.7 - Sketch the graph of a function g(y) such that the...Ch. 1.7 - Is it possible to find a continuous function...Ch. 1.7 - Prob. 18ECh. 1.7 - Consider the population model dPdt=2PP250 for a...Ch. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - Prob. 2ECh. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - Prob. 4ECh. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - Consider the nonhomogeneous linear equation...Ch. 1.8 - Prob. 14ECh. 1.8 - Prob. 15ECh. 1.8 - Prob. 16ECh. 1.8 - Consider the nonlinear differential equation...Ch. 1.8 - Prob. 18ECh. 1.8 - Prob. 19ECh. 1.8 - Consider the nonhomogeneous linear equation...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - Prob. 25ECh. 1.8 - Prob. 26ECh. 1.8 - In Exercises 25-28, give a brief qualitative...Ch. 1.8 - Prob. 28ECh. 1.8 - A person initially places $1,000 in a savings...Ch. 1.8 - A student has saved $70,000 for her college...Ch. 1.8 - A college professor contributes $5,000 per year...Ch. 1.8 - Prob. 32ECh. 1.8 - Prob. 33ECh. 1.8 - Prob. 34ECh. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 7-12, solve the given initial-value...Ch. 1.9 - In Exercises 7-12, solve the given initial-value...Ch. 1.9 - Prob. 9ECh. 1.9 - Prob. 10ECh. 1.9 - Prob. 11ECh. 1.9 - In Exercises 7-12, solve the given initial-value...Ch. 1.9 - In Exercises 13-18, the differential equation is...Ch. 1.9 - Prob. 14ECh. 1.9 - Prob. 15ECh. 1.9 - Prob. 16ECh. 1.9 - Prob. 17ECh. 1.9 - Prob. 18ECh. 1.9 - Prob. 19ECh. 1.9 - Prob. 20ECh. 1.9 - Prob. 21ECh. 1.9 - Prob. 22ECh. 1.9 - Prob. 23ECh. 1.9 - A 30-gallon tank initially contains 15 gallons of...Ch. 1.9 - A 400-gallon tank initially contains 200 gallons...Ch. 1.9 - A 100-gallon tank initially contains loo gallons...Ch. 1.9 - Suppose a 50-gallon tank contains a volume Vo of...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Prob. 4RECh. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - True-false: For Exercises 11-20, determine if the...Ch. 1 - Prob. 16RECh. 1 - True-false: For Exercises 11-20, determine if the...Ch. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - In Exercises 21-29, (a) specify if the given...Ch. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - In Exercises 30-39, (a) specify if the given...Ch. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Consider the autonomous differential equation...Ch. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Eight differential equations and four slope fields...Ch. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Consider the differential equation dy/dt=2ty2 ....Ch. 1 - Prob. 53RECh. 1 - A 1000-galIon tank initially contains a mixture of...
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
- 2 Q/Given H (x,y) = x² + y² - y² Find the Hamiltonian System and prove it is first integral-arrow_forwardQ2) A: Find the region where ODEs has no limit cycle: x = y + x³ y=x+y+y³ 6arrow_forwardQ3)A: Given H(x,y)=x2-x+ y²as a first integral of an ODEs, find this ODES corresponding to H(x,y) and show the phase portrait by using Hartman theorem and by drawing graph of H(x,y)-e. Discuss the stability of critical points of the corresponding ODEs.arrow_forward
- Which angles are complementary to each other? Select all that apply. 3 2 4 in 5 1 Z1 and 23 Z1 and 25 22 and 23 Z2 and 25 Submitarrow_forwardWhich angles are adjacent to each other? Select all that apply. 3 2 4 67 5 8 11 10 12 12 9 27 and 28 Z9 and 12 Z3 and 24 Z10 and Z11arrow_forwardIf the arc length of NMP is 11π, what is the length of MNP expressed in terms of πT? M N 5 44% ○ A. 54π OB. 108π P О с. 103 18 O D. 108arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License