Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

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Short Answer

In Problems 11–14, solve the related phase plane differential equation for the given system. Then sketch by hand several representative trajectories (with their flow arrows).
$\frac{dx}{dt} = (y - x) (y - 1) \frac{dy}{dt} = (x - y) (x - 1)$

The solution is $(y - 1)^{2} + (x - 1)^{2} = c$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find phase plane equation

Here the system is:

$\frac{d x}{d t} = (y - x) (y - 1) \frac{d y}{d t} = (x - y) (x - 1)$

And the phase plane equation is:

$\frac{d y}{d x} = \frac{(x - y) (x - 1)}{(y - x) (y - 1)} \frac{d y}{d x} = \frac{1 - x}{y - 1}$

Step 2: Solve the equation

Here the equation is $\frac{d y}{d x} = \frac{1 - x}{y - 1}$ .

Solving by variable separating. Then,

$\int (y - 1) d y = \int - (x - 1) d x {(y - 1)}^{2} + {(x - 1)}^{2} = c$

Since the solutions are centered at (1,1). And line y = x.

Step 3: Sketch some trajectories.

Therefore, the solution is $(y - 1)^{2} + (x - 1)^{2} = c$ .

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 11–14, solve the related phase plane differential equation for the given system. Then sketch by hand several representative trajectories (with their flow arrows).
$\frac{dx}{dt} = (y - x) (y - 1) \frac{dy}{dt} = (x - y) (x - 1)$

Step by Step Solution

Step 1: Find phase plane equation

Step 2: Solve the equation

Step 3: Sketch some trajectories.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 11–14, 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)

Step by Step Solution

Step 1: Find phase plane equation

Step 2: Solve the equation

Step 3: Sketch some trajectories.

Most popular questions for Math Textbooks

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In Problems 11–14, solve the related phase plane differential equation for the given system. Then sketch by hand several representative trajectories (with their flow arrows).
$\frac{dx}{dt} = (y - x) (y - 1) \frac{dy}{dt} = (x - y) (x - 1)$