Program Explanation Given information: The differential equation is d x d t = k x ( x − M ) − h and the values are H = 1 2 ( M + M 2 + 4 h / k ) > 0 and K = 1 2 ( M − M 2 + 4 h / k ) < 0 . Explanation: The given differential equation is d x d t = k x ( x − M ) − h . The critical points of the function are those pints where the derivative of the function would be 0. So put the given differential equation equals to 0 as, 0 = k x ( x − M ) − h It can be observed that that the above equation is a quadratic equation as 0 = k x 2 − k x M − h . Therefore, use the quadratic rule to find the two critical points. d x d t = k x ( x − M ) − h Therefore, the critical points are x 1 and x 2 . x 1 , x 2 = 1 2 ( M ± M 2 + 4 h k ) It can be observe that the value of the obtained critical points x 1 , x 2 is same of the value of H and K

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Concept explainers

Representation of Polynomial

It is necessary for the polynomial expression that each expression consists of two parts:

Question

Chapter 2.2, Problem 28P

Program Plan Intro

Program Description: Purpose ofproblem is to show that the differential equation dxdt=kx(x−M)−h can be rewritten as dxdt=k(x−H)(x−K) where H=12(M+M2+4h/k)>0 and K=12(M−M2+4h/k)<0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.2, Problem 27P

Chapter 2.2, Problem 29P

Students have asked these similar questions

I would like to know the main features about the following 3 key concepts:1. Backup Domain Controller (BDC)2. Access Control List (ACL)3. Dynamic Memory

In cell C21, enter a formula to calculate the number of miles you expect to drive each month. Divide the value of number of miles (cell A5 from the Data sheet) by the average MPG for the vehicle multiplied by the price of a gallon of gas (cell A6 from the Data sheet).

Microsoft Excel

Chapter 2 Solutions

EBK DIFFERENTIAL EQUATIONS

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

Ch. 2.1 - Prob. 11P Ch. 2.1 - Prob. 12P Ch. 2.1 - Prob. 13P Ch. 2.1 - Prob. 14P Ch. 2.1 - Prob. 15P Ch. 2.1 - Prob. 16P Ch. 2.1 - Prob. 17P Ch. 2.1 - Prob. 18P Ch. 2.1 - Prob. 19P Ch. 2.1 - Prob. 20P Ch. 2.1 - Prob. 21P Ch. 2.1 - Suppose that at time t=0, half of a logistic...Ch. 2.1 - Prob. 23P Ch. 2.1 - Prob. 24P Ch. 2.1 - Prob. 25P Ch. 2.1 - Prob. 26P Ch. 2.1 - Prob. 27P Ch. 2.1 - Prob. 28P Ch. 2.1 - Prob. 29P Ch. 2.1 - A tumor may be regarded as a population of...Ch. 2.1 - Prob. 31P Ch. 2.1 - Prob. 32P Ch. 2.1 - Prob. 33P Ch. 2.1 - Prob. 34P Ch. 2.1 - Prob. 35P Ch. 2.1 - Prob. 36P Ch. 2.1 - Prob. 37P Ch. 2.1 - Fit the logistic equation to the actual U.S....Ch. 2.1 - Prob. 39P Ch. 2.2 - Prob. 1P Ch. 2.2 - Prob. 2P Ch. 2.2 - Prob. 3P Ch. 2.2 - Prob. 4P Ch. 2.2 - Prob. 5P Ch. 2.2 - Prob. 6P Ch. 2.2 - Prob. 7P Ch. 2.2 - Prob. 8P Ch. 2.2 - Prob. 9P Ch. 2.2 - Prob. 10P Ch. 2.2 - Prob. 11P Ch. 2.2 - Prob. 12P Ch. 2.2 - Prob. 13P Ch. 2.2 - Prob. 14P Ch. 2.2 - Prob. 15P Ch. 2.2 - Prob. 16P Ch. 2.2 - Prob. 17P Ch. 2.2 - Prob. 18P Ch. 2.2 - Prob. 19P Ch. 2.2 - Prob. 20P Ch. 2.2 - Prob. 21P Ch. 2.2 - Prob. 22P Ch. 2.2 - Prob. 23P Ch. 2.2 - Prob. 24P Ch. 2.2 - Use the alternatives forms...Ch. 2.2 - Prob. 26P Ch. 2.2 - Prob. 27P Ch. 2.2 - Prob. 28P Ch. 2.2 - Consider the two differentiable equation...Ch. 2.3 - The acceleration of a Maserati is proportional to...Ch. 2.3 - Prob. 2P Ch. 2.3 - Prob. 3P Ch. 2.3 - Prob. 4P Ch. 2.3 - Prob. 5P Ch. 2.3 - Prob. 6P Ch. 2.3 - Prob. 7P Ch. 2.3 - Prob. 8P Ch. 2.3 - A motorboat weighs 32,000 lb and its motor...Ch. 2.3 - A woman bails out of an airplane at an altitude of...Ch. 2.3 - According to a newspaper account, a paratrooper...Ch. 2.3 - Prob. 12P Ch. 2.3 - Prob. 13P Ch. 2.3 - Prob. 14P Ch. 2.3 - Prob. 15P Ch. 2.3 - Prob. 16P Ch. 2.3 - Prob. 17P Ch. 2.3 - Prob. 18P Ch. 2.3 - Prob. 19P Ch. 2.3 - Prob. 20P Ch. 2.3 - Prob. 21P Ch. 2.3 - Suppose that =0.075 (in fps units, with g=32ft/s2...Ch. 2.3 - Prob. 23P Ch. 2.3 - The mass of the sun is 329,320 times that of the...Ch. 2.3 - Prob. 25P Ch. 2.3 - Suppose that you are strandedâ€”your rocket engine...Ch. 2.3 - Prob. 27P Ch. 2.3 - (a) Suppose that a body is dropped (0=0) from a...Ch. 2.3 - Prob. 29P Ch. 2.3 - Prob. 30P Ch. 2.4 - Prob. 1P Ch. 2.4 - Prob. 2P Ch. 2.4 - Prob. 3P Ch. 2.4 - Prob. 4P Ch. 2.4 - Prob. 5P Ch. 2.4 - Prob. 6P Ch. 2.4 - Prob. 7P Ch. 2.4 - Prob. 8P Ch. 2.4 - Prob. 9P Ch. 2.4 - Prob. 10P Ch. 2.4 - Prob. 11P Ch. 2.4 - Prob. 12P Ch. 2.4 - Prob. 13P Ch. 2.4 - Prob. 14P Ch. 2.4 - Prob. 15P Ch. 2.4 - Prob. 16P Ch. 2.4 - Prob. 17P Ch. 2.4 - Prob. 18P Ch. 2.4 - Prob. 19P Ch. 2.4 - Prob. 20P Ch. 2.4 - Prob. 21P Ch. 2.4 - Prob. 22P Ch. 2.4 - Prob. 23P Ch. 2.4 - Prob. 24P Ch. 2.4 - Prob. 25P Ch. 2.4 - Prob. 26P Ch. 2.4 - Prob. 27P Ch. 2.4 - Prob. 28P Ch. 2.4 - Prob. 29P Ch. 2.4 - Prob. 30P Ch. 2.4 - Prob. 31P Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P Ch. 2.5 - Prob. 11P Ch. 2.5 - Prob. 12P Ch. 2.5 - Prob. 13P Ch. 2.5 - Prob. 14P Ch. 2.5 - Prob. 15P Ch. 2.5 - Prob. 16P Ch. 2.5 - Prob. 17P Ch. 2.5 - Prob. 18P Ch. 2.5 - Prob. 19P Ch. 2.5 - Prob. 20P Ch. 2.5 - Prob. 21P Ch. 2.5 - Prob. 22P Ch. 2.5 - Prob. 23P Ch. 2.5 - Prob. 24P Ch. 2.5 - Prob. 25P Ch. 2.5 - Prob. 26P Ch. 2.5 - Prob. 27P Ch. 2.5 - Prob. 28P Ch. 2.5 - Prob. 29P Ch. 2.5 - Prob. 30P Ch. 2.6 - Prob. 1P Ch. 2.6 - Prob. 2P Ch. 2.6 - Prob. 3P Ch. 2.6 - Prob. 4P Ch. 2.6 - Prob. 5P Ch. 2.6 - Prob. 6P Ch. 2.6 - Prob. 7P Ch. 2.6 - Prob. 8P Ch. 2.6 - Prob. 9P Ch. 2.6 - Prob. 10P Ch. 2.6 - Prob. 11P Ch. 2.6 - Prob. 12P Ch. 2.6 - Prob. 13P Ch. 2.6 - Prob. 14P Ch. 2.6 - Prob. 15P Ch. 2.6 - Prob. 16P Ch. 2.6 - Prob. 17P Ch. 2.6 - Prob. 18P Ch. 2.6 - Prob. 19P Ch. 2.6 - Prob. 20P Ch. 2.6 - Prob. 21P Ch. 2.6 - Prob. 22P Ch. 2.6 - Prob. 23P Ch. 2.6 - Prob. 24P Ch. 2.6 - Prob. 25P Ch. 2.6 - Prob. 26P Ch. 2.6 - Prob. 27P Ch. 2.6 - Prob. 28P Ch. 2.6 - Prob. 29P Ch. 2.6 - Prob. 30P

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Program Description: Purpose ofproblem is to show that the differential equation d x d t = k x ( x − M ) − h can be rewritten as d x d t = k ( x − H ) ( x − K ) where H = 1 2 ( M + M 2 + 4 h / k ) > 0 and K = 1 2 ( M − M 2 + 4 h / k ) < 0 .

Solution Summary: The author explains that the differential equation can be rewritten as dx. The critical points are those pints where the derivative of the function would be 0.

Concept explainers

Program Description: Purpose ofproblem is to show that the differential equation dxdt=kx(x−M)−h can be rewritten as dxdt=k(x−H)(x−K) where H=12(M+M2+4h/k)>0 and K=12(M−M2+4h/k)<0 .

Want to see the full answer?

Chapter 2 Solutions

Program Description: Purpose ofproblem is to show that the differential equation d x d t = k x ( x − M ) − h can be rewritten as d x d t = k ( x − H ) ( x − K ) where H = 1 2 ( M + M 2 + 4 h / k ) &gt; 0 and K = 1 2 ( M − M 2 + 4 h / k ) &lt; 0 .

Solution Summary: The author explains that the differential equation can be rewritten as dx. The critical points are those pints where the derivative of the function would be 0.

Concept explainers

Program Description: Purpose ofproblem is to show that the differential equation dxdt=kx(x−M)−h can be rewritten as dxdt=k(x−H)(x−K) where H=12(M+M2+4h/k)>0 and K=12(M−M2+4h/k)<0 .

Want to see the full answer?

Chapter 2 Solutions

Program Description: Purpose ofproblem is to show that the differential equation d x d t = k x ( x − M ) − h can be rewritten as d x d t = k ( x − H ) ( x − K ) where H = 1 2 ( M + M 2 + 4 h / k ) > 0 and K = 1 2 ( M − M 2 + 4 h / k ) < 0 .