Differential Equations
4th Edition
ISBN: 9781133383093
Author: Paul Blanchard; Robert L. Devaney; Glen R. Hall
Publisher: Cengage Learning US
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Chapter 2.3, Problem 5E
(a)
To determine
To sketch the associated direction field using HPG system solver.
(b)
To determine
To calculate:the two non-zero solutions that are not multiples of one another using the guess and test method.
(c)
To determine
To plot the solution curve in the yv-plane and its y(t) and v(t) graphs.
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Exercise 11.3 A slope field is given for the equation y' = 4y+4.
(a) Sketch the particular solution that corresponds to y(0) = −2
(b) Find the constant solution
(c) For what initial conditions y(0) is the solution increasing?
(d) For what initial conditions y(0) is the solution decreasing?
(e) Verify these results using only the differential equation y' = 4y+4.
Chapter 2 Solutions
Differential Equations
Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Exercises 1-6 refer to the following systems of...Ch. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Consider the predator-prey system...Ch. 2.1 - Consider the predator-prey system dRdt=2R(1R...Ch. 2.1 - Exercises 9-14 refer to the predator-prey and the...Ch. 2.1 - Exercises 9-14 refer to the predator-prey and the...
Ch. 2.1 - Exercises 9-14 refer to the predator-prey and the...Ch. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Exercises 9-14 refer to the predator-prey and the...Ch. 2.1 - Prob. 15ECh. 2.1 - Consider the system of predator-prey equations...Ch. 2.1 - Pesticides that kill all insect species are not...Ch. 2.1 - Some predator species seldom capture healthy adult...Ch. 2.1 - Prob. 19ECh. 2.1 - Consider the initial-value problem d2ydt2+kmy=0...Ch. 2.1 - A mass weighing 12 pounds stretches a spring 3...Ch. 2.1 - A mass weighing 4 pounds stretches a spring 4...Ch. 2.1 - Do the springs in an “extra firm’ mattress have a...Ch. 2.1 - Consider a vertical mass-spring system as shown in...Ch. 2.1 - Exercises 25—30 refer to a situation in which...Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Exercises 25—30 refer to a situation in which...Ch. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Convert the second-order differential equation 1...Ch. 2.2 - Prob. 9ECh. 2.2 - Consider the system dxdt=2x+ydydt=2y and its...Ch. 2.2 - Eight systems of differential equations and four...Ch. 2.2 - Consider the modified predator-prey system...Ch. 2.2 - In Exercises 13—18. (a) find the equilibrium...Ch. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - In Exercises 13—18. (a) find the equilibrium...Ch. 2.2 - Prob. 17ECh. 2.2 - In Exercises 13—18. (a) find the equilibrium...Ch. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Consider the four solution curves in the phase...Ch. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - In Exercises 1—4, a harmonic oscillator equation...Ch. 2.3 - Prob. 5ECh. 2.3 - In the damped harmonic oscillator, we assume that...Ch. 2.3 - Consider any damped harmonic oscillator equation...Ch. 2.3 - Consider any damped harmonic oscillator equation...Ch. 2.3 - In Exercises 9 and 10, we consider a mass sliding...Ch. 2.3 - In Exercises 9 and 10, we consider a mass sliding...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 1-4, we consider the system...Ch. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - Prob. 6ECh. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - Prob. 8ECh. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - In Exercises 5-12, we consider the partially...Ch. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Consider the partially decoupled system...Ch. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - In Exercises 3—6, a system, an initial condition,...Ch. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Using a computer or calculator, apply Euler’s...Ch. 2.5 - Prob. 8ECh. 2.6 - Consider the system dxdt=x+ydydt=y (a) Show that...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - (a) Suppose Y1(t) is a solution of an autonomous...Ch. 2.6 - Prob. 9ECh. 2.6 - Consider the system dxdt=2dydt=y2 (a) Calculate...Ch. 2.6 - Consider the system dxdt=2dydt=y2 Show that, for...Ch. 2.7 - Prob. 1ECh. 2.7 - In the SIR model, we assume that everyone in the...Ch. 2.7 - Vaccines make it possible to prevent epidemics....Ch. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - One of the basic assumptions of the SIR model is...Ch. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - Using =1.66 and the value of that you determined...Ch. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2 - Prob. 1RECh. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Short answer exercises: Exercises 1-14 focus on...Ch. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - In Exercises 31-34, a solution curve in the...Ch. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Consider the partially decoupled system...Ch. 2 - Consider the partially decoupled system...Ch. 2 - Prob. 37RE
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