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

The direction field for $\frac{dy}{dx} = 2 x + y$ as shown in figure 1.13.
Sketch the solution curve that passes through (0, -2). From this sketch, write the equation for the solution.
b. Sketch the solution curve that passes through (-1, 3).
c. What can you say about the solution in part (b) as $x \to + \infty$ ? How about $x \to - \infty$ ?

The graph is drawn below, and the equation is $y = - 2 - 2 x$ .
The graph is drawn below, and the equation is $y = 1 - 2 x$ .
The solutions become infinite when $x \to + \infty or x \to - \infty$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1(a): Find the curve by point (0,-2)

Given $\frac{dy}{dx} = 2 x + y . . . . . . (1)$

Put the value of the point (0,-2) in equation (1)

$m = 2 (0) - 2 = - 2$

The curve is $(y + 2) = - 2 (x - 0)$

Hence the solution is $y = - 2 - 2 x$ .

By putting the different values of x, get the values of y.

Step 2(b): Find the curve by point (-1,3).

Given $\frac{dy}{dx} = 2 x + y . . . . . . (2)$

Put the value of the point (-1,3) in equation (2)

$m = 2 (- 1) - 3 = 1$

The curve is $y = 1 - 2 x$

Hence the solution is $y = 1 - 2 x$ .

Step 3(c): Discuss the solution in part (b) as x→+∞ and x→-∞

As $x \to \infty$ the solution becomes infinite. And when $x \to - \infty$ the solution also becomes infinite and has an asymptote $y = - 2 - 2 x$ .

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Step by Step Solution

Step 1(a): Find the curve by point (0,-2)

Step 2(b): Find the curve by point (-1,3).

Step 3(c): Discuss the solution in part (b) as x→+∞ and x→-∞

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Step by Step Solution

Step 1(a): Find the curve by point (0,-2)

Step 2(b): Find the curve by point (-1,3).

Step 3(c): Discuss the solution in part (b) as x→+∞ and x→-∞

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