Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Question: In Problems 1–10, determine all the singular points of the given differential equation.
4. (x²+x)y"+3y'-6xy = 0

The singular point exists in this differential equation for both ^P(x) and ^Q(x) is at x = 0,-1

See the step by step solution

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 y"+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,

(x²+x)y"+3y-6xy = 0

Dividing the above equation by (x²+x)we get,

y"+ $\frac{3}{(x^{2} + x)} y' - \frac{6 x}{(x^{2} + x)} y = 0$

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

P(x) = $\frac{3}{x (x + 1)}$

Q(x) = $- \frac{6 x}{x (x + 1)}$

= $- \frac{6}{(x + 1)}$ ..................................(1)

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

For ^P(x) this occurs at x = 0,-1 .

We see that ^Q(x) is actually analytic at x = 0 .

Since we can cancel an x in the numerator and denominator of ^Q(x⁾ as shown in (1).

Therefore, ^P(x) is analytic except at x = 0,-1 as well as ^Q(x) is analytic except at x = -1 .

The singular point exists in this differential equation for both ^P(x) and ^Q(x) is at x = 0,-1 .

Find Study Materials for

Create Study Materials

Select your language

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.
4. (x²+x)y"+3y'-6xy = 0

Step by Step Solution

Step 1: Ordinary and Singular Points

Step 2: Find the singular points

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

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.4. (x2+x)y"+3y'-6xy = 0

Step by Step Solution

Step 1: Ordinary and Singular Points

Step 2: Find the singular points

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Question: In Problems 1–10, determine all the singular points of the given differential equation.
4. (x²+x)y"+3y'-6xy = 0