BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Use power series to solve the differential equation.

3. y' = x2y

To determine

To solve: The differential equation by the use of power series.

Explanation

Given data:

The differential equation is,

yx2y=0 (1)

Consider the expression for y(x) .

y(x)=n=0cnxn (2)

Differentiate equation (2) with respect to t.

y(x)=n=1ncnxn1

y(x)=n=0(n+1)cn+1xn (3)

Multiply x2 on both sides of equation (2).

x2y=n=0cnxn+2

x2y=n=2cn2xn (4)

Substitute equations (3) and (4) in equation (1),

n=0(n+1)cn+1xnn=2cn2xn=0

Rewrite the expression,

c1+2c2x+n=2[(n+1)cn+1cn2]xn=0 (5)

From equation (5), equating coefficients gives,

c1=0 and c2=0

Equation (5) is true when the coefficients of xn are 0. Therefore, the required expression is,

(n+1)cn+1cn2=0 (6)

Re-arrange the equation.

cn+1=cn2(n+1)

cn+1=cn2(n+1),n=2,3, (7)

Equation (7) is the recursion relation.

Solve the recursion relation by substituting n=2,3 in equation (7).

Substitute 2 for n in equation (7),

cn+1=cn2(n+1)c2+1=c22(2+1)c3=c03

c3=c03 (8)

Substitute 3 for n in equation (7),

c3+1=c32(3+1)c4=c14

Substitute 0 for c1 ,

c4=04

c4=0 (9)

Substitute 4 for n in equation (7),

c4+1=c42(4+1)c5

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 17 Solutions

Show all chapter solutions add
Sect-17.1 P-11ESect-17.1 P-12ESect-17.1 P-13ESect-17.1 P-14ESect-17.1 P-15ESect-17.1 P-16ESect-17.1 P-17ESect-17.1 P-18ESect-17.1 P-19ESect-17.1 P-20ESect-17.1 P-21ESect-17.1 P-22ESect-17.1 P-23ESect-17.1 P-24ESect-17.1 P-25ESect-17.1 P-26ESect-17.1 P-27ESect-17.1 P-28ESect-17.1 P-29ESect-17.1 P-30ESect-17.1 P-31ESect-17.1 P-32ESect-17.1 P-33ESect-17.1 P-34ESect-17.2 P-1ESect-17.2 P-2ESect-17.2 P-3ESect-17.2 P-4ESect-17.2 P-5ESect-17.2 P-6ESect-17.2 P-7ESect-17.2 P-8ESect-17.2 P-9ESect-17.2 P-10ESect-17.2 P-11ESect-17.2 P-12ESect-17.2 P-13ESect-17.2 P-14ESect-17.2 P-15ESect-17.2 P-16ESect-17.2 P-17ESect-17.2 P-18ESect-17.2 P-19ESect-17.2 P-20ESect-17.2 P-21ESect-17.2 P-22ESect-17.2 P-23ESect-17.2 P-24ESect-17.2 P-25ESect-17.2 P-26ESect-17.2 P-27ESect-17.2 P-28ESect-17.3 P-1ESect-17.3 P-2ESect-17.3 P-3ESect-17.3 P-4ESect-17.3 P-5ESect-17.3 P-6ESect-17.3 P-7ESect-17.3 P-8ESect-17.3 P-9ESect-17.3 P-10ESect-17.3 P-11ESect-17.3 P-12ESect-17.3 P-13ESect-17.3 P-14ESect-17.3 P-15ESect-17.3 P-16ESect-17.3 P-17ESect-17.3 P-18ESect-17.4 P-1ESect-17.4 P-2ESect-17.4 P-3ESect-17.4 P-4ESect-17.4 P-5ESect-17.4 P-6ESect-17.4 P-7ESect-17.4 P-8ESect-17.4 P-9ESect-17.4 P-10ESect-17.4 P-11ESect-17.4 P-12ECh-17 P-1RCCCh-17 P-2RCCCh-17 P-3RCCCh-17 P-4RCCCh-17 P-5RCCCh-17 P-1RQCh-17 P-2RQCh-17 P-3RQCh-17 P-4RQCh-17 P-1RECh-17 P-2RECh-17 P-3RECh-17 P-4RECh-17 P-5RECh-17 P-6RECh-17 P-7RECh-17 P-8RECh-17 P-9RECh-17 P-10RECh-17 P-11RECh-17 P-12RECh-17 P-13RECh-17 P-14RECh-17 P-15RECh-17 P-16RECh-17 P-17RECh-17 P-18RECh-17 P-19RECh-17 P-20RECh-17 P-21RE

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 39-44, write the equation in the slope-intercept form and then find the slope and y-intercept of t...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problems 37-44, perform the indicated operations and simplify. 40.

Mathematical Applications for the Management, Life, and Social Sciences

Find dy/dx by implicit differentiation. 9. x2x+y=y2+1

Single Variable Calculus: Early Transcendentals

Proof Prove Property 3 of Theorem 2.1. (You may use Property 3 of Theorem 2.2.)

Calculus: Early Transcendental Functions (MindTap Course List)

True or False: The x-intercepts are the values of x for which f(x) = 0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The graph of x = cos t, y = sin2 t is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 1320, plot the point on a set of coordinate axes. (52,32)

Finite Mathematics for the Managerial, Life, and Social Sciences

Define the concept of external validity and a threat to external validity.

Research Methods for the Behavioral Sciences (MindTap Course List)