/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q27E Using the software, sketch the d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q27E (page 272)

Using the software, sketch the direction field in the phase-plane for the system dxdt=-2x+y,dydt=-5x-4y. From the sketch, predict the asymptotic limit (ast鈫�鈭�

of the solution starting at (1, 1).

Short Answer

Expert verified

The solution starts at (1,1) and moves towards zero as t鈫�鈭� the solution approaches to (0,0).

Step by step solution

01

Find the critical point

Here the equation is:

dxdt=-2x+ydydt=-5x-4y

And

dydx=-5x-4y-2x+y

The solution starts at (1,1) and moves towards zero as the solution approaches to (0,0).

02

Sketch the Directional field

This is the required result.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 11鈥�14, solve the related phase plane differential equation for the given system. Then sketch by hand several representative trajectories (with their flow arrows).

dxdt=(y-x)(y-1)dydt=(x-y)(x-1)

In Problems 3 鈥� 18, use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.

x''+y''-x'=2t,x''+y'-x+y=-1

Logistic Model.In Section 3.2 we discussed the logistic equation\(\frac{{{\bf{dp}}}}{{{\bf{dt}}}}{\bf{ = A}}{{\bf{p}}_{\bf{1}}}{\bf{p - A}}{{\bf{p}}^{\bf{2}}}{\bf{,p(0) = }}{{\bf{p}}_{\bf{o}}}\)and its use in modeling population growth. A more general model might involve the equation\(\frac{{{\bf{dp}}}}{{{\bf{dt}}}}{\bf{ = A}}{{\bf{p}}_{\bf{1}}}{\bf{p - A}}{{\bf{p}}^{\bf{r}}}{\bf{,p(0) = }}{{\bf{p}}_{\bf{o}}}\)where r>1. To see the effect of changing the parameter rin (25), take \({{\bf{p}}_{\bf{1}}}\)= 3, A= 1, and \({{\bf{p}}_{\bf{o}}}\)= 1. Then use a numerical scheme such as Runge鈥揔utta with h= 0.25 to approximate the solution to (25) on the interval\(0 \le {\bf{t}} \le 5\) for r= 1.5, 2, and 3What is the limiting population in each case? For r>1, determine a general formula for the limiting population.

In Problems 3鈥�6, find the critical point set for the given system.

dxdt=x-y,dydt=x2+y2-1

For the interconnected tanks problem of Section5.1, page241, suppose that instead of pure water being fed into the tankA, a brine solution with concentration0.2kg/L is used; all other data remain the same. Determine the mass of salt in each tank at time tif the initial masses are and y0=0.3kg.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.