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 3–6, find the critical point set for the given system.
$\frac{dx}{dt} = x - y, \frac{dy}{dt} = x^{2} + y^{2} - 1$

The critical points are $(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}), (- \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find critical points

Consider the system as:

$\frac{d x}{d t} = x - y \frac{d y}{d t} = x^{2} + y^{2} - 1$

For finding the critical points put the system equal to 0.

So,

$\begin{array}{rcl} x - y & = & 0 \\ x & = & y \\ x^{2} + y^{2} - 1 & = & 0 \\ x^{2} + y^{2} & = & 1 \end{array}$

Step 2: Solve for x and y

Put the value of y in another equation and solve, then;

$\begin{array}{rcl} x^{2} + x^{2} & = & 1 \\ 2 x^{2} & = & 1 \\ x & = & \pm \frac{1}{\sqrt{2}} \end{array}$

Thus, the critical points are $(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}), (- \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$ .

This is the required result.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 3–6, find the critical point set for the given system.
$\frac{dx}{dt} = x - y, \frac{dy}{dt} = x^{2} + y^{2} - 1$

Step by Step Solution

Step 1: Find critical points

Step 2: Solve for x and y

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 3–6, find the critical point set for the given system.dxdt=x-y,dydt=x2+y2-1

Step by Step Solution

Step 1: Find critical points

Step 2: Solve for x and y

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In Problems 3–6, find the critical point set for the given system.
$\frac{dx}{dt} = x - y, \frac{dy}{dt} = x^{2} + y^{2} - 1$