Chapter 17.2, Problem 6E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Solve the differential equation or initial-value problem using the method of undetermined coefficients.

**6.** *y"* – 4*y'* + 4y = *x* – sin *x*

To determine

**To solve:** The differential equation by the method of undetermined coefficients.

Explanation

**Given data:**

The differential equation is,

Consider the auxiliary equation is,

Roots of equation (2) are,

Write the expression for the complementary solution,

Re-write equation (1) by neglecting the term

The particular solution

Differentiate equation (4) with respect to *x*,

Differentiate equation (5) with respect to *x*,

Substitute equations (4), (5) and (6) in (3),

Differentiate the equation (7) with respect to *x*,

Simplify the equation,

Substitute 0 for *x* in equation (7),

Substitute
*A* in equation (8),

Substitute
*A* and
*B* in equation (4),

Re-write equation (1) by neglecting *x*.

The particular solution

Differentiate equation (11) with respect to *x*,

Differentiate equation (12) with respect to *x*,

Sect-17.1 P-1ESect-17.1 P-2ESect-17.1 P-3ESect-17.1 P-4ESect-17.1 P-5ESect-17.1 P-6ESect-17.1 P-7ESect-17.1 P-8ESect-17.1 P-9ESect-17.1 P-10E

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

Single Variable Calculus: Early Transcendentals, Volume I

Precalculus: Mathematics for Calculus (Standalone Book)

Finite Mathematics and Applied Calculus (MindTap Course List)

Multivariable Calculus

Calculus: Early Transcendental Functions

Calculus: An Applied Approach (MindTap Course List)

Essentials Of Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Applied Calculus

Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus

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

Understanding Basic Statistics

Probability and Statistics for Engineering and the Sciences

Finite Mathematics

Elementary Geometry For College Students, 7e

Mathematical Excursions (MindTap Course List)

Intermediate Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Elementary Technical Mathematics

Single Variable Calculus: Early Transcendentals

Calculus of a Single Variable

Elements Of Modern Algebra

Trigonometry (MindTap Course List)

Contemporary Mathematics for Business & Consumers

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

Study Guide for Stewart's Multivariable Calculus, 8th

Calculus: Early Transcendental Functions (MindTap Course List)

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences