The number 0 is a critical point of the autonomous differential equation dx/dt = x n ,

Question:

The number 0 is a critical point of the autonomous differential equation dx/dt = xⁿ, where n is a positive integer. For what values of n is 0 asymptotically stable? Semi-stable? Unstable? Repeat for the differential equation dx/dt = 2xⁿ.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course in Differential Equations with Modeling Applications

ISBN: 978-1305965720

11th edition

Authors: Dennis G. Zill

See More Books

Question Posted: Jul 09, 2018 01:56 PM

See More Questions

Consider the autonomous differential equation dy/dx = f (y), where the graph of f is given. Use the graph to locate the critical points of each differential equation. Sketch a phase portrait of each...
Suppose the model in Problem 40 is modied so that air resistance is proportional to v 2 , that is, M dv/dt = mg - kv 2 . See Problem 17 in Exercises 1.3. Use a phase portrait to find the terminal...
A point x0 is a critical point of a C1 functional if and only if
Retro Games (RG) based in Nevada, manufactures gaming equipment. On January 1, 2019, RG began to aggressively expand its remote sales force, which included hiring Tom in Ohio to sell in that state....
1. Define indigenous religion, and describe at least one aspect of indigenous religions that exists in a similar form in a traditional mainstream religion. Define religion, and discuss why it is...
Mensa Mountaineering Company (MMC) provides guided mountain climbing expeditions in the Rocky Mountains. Its only major expense is guide salaries; it pays each guide $$4,800$ per climbing...
palmes
Rush Presbyterian requires that employees in all job classifications be able to speak and write English. Garcia, a Latino, contends that this rule discriminates against those for whom English is not...
Which of the following statements is NOT true concerning the Other Dependent Credit Choose one answer. a. The credit was first available in 2018. b. Residents of Canada meet the definition as a...
You work in the human resources department of your company helping new employees fill out the necessary paperwork to get their first paycheck. There are a number of decisions that employees must make...
Solve the given differential equation. (y 2 + 1 dx) = y sec 2 xdy
Construct an autonomous first order differential equation dy/dx = f (y) whose phase portrait is consistent with the given figure. 4
A - beam is brought to rest in a liquid hydrogen target. Here 0 are produced by the charge exchange reaction - + p 0 + n. Find the energy of the 0 , the kinetic energy of the n, the velocity of...
1- What is the chairman of the Texas State Board of Education's primary occupation? 2- Why are the decisions the Texas State Board of Education make about their high school science standards so...
SECTION 7 KEEPING ENTIRE STRUCTURES IN EQUILIBRIUM ASSIGNMENT #2 1. Find the reactions at A and C. A 2. Find the reactions at A and C. 60.0 kN B 3.00 9.00 4.00 6.00 5.00 kN 3.00 B 1.00 2.00 10.0 kN...
The year-end financial statements of Python Tax Services are provided below. Service revenue Expenses: Salaries Utilities Insurance Supplies Net income PYTHORT TAX SERVICES Income Statement $ 68,500...
a. Calculate the volume of the solid of revolution created by rotating the curve y=2+4 exp(-5 x) about the x-axis, for x between 2 and 4. Volume: b. The equation of a circle of radius r, centered at...
The simply supported timber beam of Figure 1 is made-up by gluing together three 300 mm by 150 mm planks as shown. The beam has to carry a uniformly distributed vertically downward load of 8 kN/m for...
For the matrices (a) Find k such that Nul A is a subspace of R k , (b) Find k such that Col A is a subspace of R k . A = [1 -3 9 0 5]
Prove that if Σ an is absolutely convergent, then a. an
In Problem 35 find a solution of the BVP when f(x) = 1. Problem 35 In problems, (a) Use (27) and (28) to find a solution of the boundary-value problem. (b) Verify that the function y p (x) satisfies...
In problem 36 find a solution of the BVP when f(x) = x. Problem 36 In problems, (a) Use (27) and (28) to find a solution of the boundary-value problem. (b) Verify that the function y p (x) satisfies...
In problem proceed as in Examples 7 and 8 to find a solution of the given boundary value problem. y'' + y = 1, y(0) = 0, y(1) = 0
Indicate whether the following managerial policy increases the risk of a death spiral:Use of low operating leverage for productionGroup of answer choicesTrueFalse
It is typically inappropriate to include the costs of excess capacity in product prices; instead, it should be written off directly to an expense account.Group of answer choicesTrueFalse
Firms can avoid the death spiral by excluding excess capacity from their activity bases. Group of answer choicesTrueFalse

The number 0 is a critical point of the autonomous differential equation dx/dt = x n ,

Question:

Step by Step Answer:

n oold dx dt x n Hence o is unstable Critical point For d...View the full answer

A First Course in Differential Equations with Modeling Applications

Students also viewed these Mathematics questions