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 problem $1 - 6$ , determine whether the differential equation is separable $\frac{dy}{dx} - s i n (x + y) = 0$ .

The differential equation $\frac{d y}{d x} - \sin (x + y) = 0$ is not separable.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concept of Separable Differential Equation

A first-order ordinary differential equation $\frac{d y}{d x} = f (x, y)$ is referred to as separable if the function in the right-hand side of the equation is expressed as a product of two functions $g (x)$ that is a function of $x$ alone and $h (y)$ that is a function of $y$ alone.

Mathematically, the equation is $\frac{d y}{d x} = f (x, y)$ separable, when $f (x y) = g (x) h (y)$

Step 2: Determining whether the equation is Separable or not

The given equation is

$\frac{d}{d x} - \sin (x + y) = 0 . . . . . . (1)$

Write the given equation as follows:

role="math" localid="1654761564667" $\frac{d}{d x} = \sin (x + y) . . . . . . (2)$

Now, use the trigonometrical to identity $\sin (A + B) = \sin A \cos B = \cos A \sin B$ . It results,

$\sin (x + y) = \sin x \cos y + \cos x \sin y$

In this case, equation (2) becomes,

$\frac{d y}{d x} = \sin x \cos y + \cos x \sin y . . . . . . . . (3)$

The function in the right – hand side of equation (3) is

$f (x, y) = \sin x \cos y + \cos x \sin y$

This function can’t be written as a product of two functions $g (x)$ and $h (y)$ .

Therefore, the given differential equation is not separable.

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

In problem $1 - 6$ , determine whether the differential equation is separable $\frac{dy}{dx} - s i n (x + y) = 0$ .

Step by Step Solution

Step 1: Concept of Separable Differential Equation

Step 2: Determining whether the equation is Separable or not

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In problem 1-6 , determine whether the differential equation is separable dydx-sin(x+y)=0.

Step by Step Solution

Step 1: Concept of Separable Differential Equation

Step 2: Determining whether the equation is Separable or not

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In problem $1 - 6$ , determine whether the differential equation is separable $\frac{dy}{dx} - s i n (x + y) = 0$ .