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 role="math" localid="1654775979001" $(x y^{2} + 3 y^{2}) d y - 2 x d x = 0$ .

The differential equation $(x y^{2} + 3 y^{2}) d y - 2 x d x = 0$ is 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 alone.

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

Step 2: Determining whether the equation is Separable or not

The given equation is

$(x y^{2} + 3 y^{2}) d y - 2 x d x = 0 . . . . . . . . . . (1)$

Equation (i) can be written as

$y^{2} (x + 3) d y - 2 x d x = 0 \frac{d y}{d x} = \frac{2 x}{y^{2} (x + 3)}$

The function in the right – hand side of equation (1) is

$f (x, y) = \frac{2 x}{y^{2} (x + 3)} = \frac{2 x}{x^{2} + 3} \frac{1}{y^{2}}$

This function can be written as a product of two functions $g (x)$ and $h (y)$ defined as,

$g (x) = \frac{2 x}{x^{2} + 3} = \frac{1}{y^{2}}$

Therefore, the given differential equation is 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 role="math" localid="1654775979001" $(x y^{2} + 3 y^{2}) d y - 2 x d x = 0$ .

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 role="math" localid="1654775979001" (xy2+3y2)dy-2x dx=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 role="math" localid="1654775979001" $(x y^{2} + 3 y^{2}) d y - 2 x d x = 0$ .