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

Question: In Problems 1–10, determine all the singular points of the given differential equation.
2. x²y"-3y-xy = 0

The only singularity point exists in this differential equation for both ^P(x) and ^Q(x) is at ^{x = 0}.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Ordinary and Singular Points.

A point ^$x_{0}$ is called an ordinary point of equation u"+p(x)y'+q(x)y = 0 if both p and q are analytic at ^$x_{0}$ . If ^$x_{0}$ is not an ordinary point, it is called a singular point of the equation.

Step 2: Find the singular points.

The given differential equation is

x²y"-3y'-xy = 0

Dividing the above equation by x²we get,

$y " - \frac{3}{x^{2}} y' - \frac{x}{x^{2}} y = 0$

On comparing the above equation with y"+p(x)y'+q(x)y = 0, we find that,

P(x)= $- \frac{3}{x^{2}}$

Q(x) = $- \frac{x}{x^{2}}$

= $- \frac{1}{x}$

Hence, ^P(x) and ^Q(x) are analytic except, perhaps, when their denominators are zero.

For ^P(x) this occurs at ^{x = 0}.

We see that ^P(x) is actually analytic at ^{x = 0} as well as ^Q(x) is analytic except at ^{x = 0}.

The only singularity point exists in this differential equation for both ^P(x) and Q(x) is at ^{x = 0}.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Question: In Problems 1–10, determine all the singular points of the given differential equation.
2. x²y"-3y-xy = 0

Step by Step Solution

Step 1: Ordinary and Singular Points.

Step 2: Find the singular points.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Question: In Problems 1–10, determine all the singular points of the given differential equation.2. x2y"-3y-xy = 0

Step by Step Solution

Step 1: Ordinary and Singular Points.

Step 2: Find the singular points.

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Question: In Problems 1–10, determine all the singular points of the given differential equation.
2. x²y"-3y-xy = 0