Chapter 17.2, Problem 8E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

**8.** *y"* – *y'* = *xe*^{2x}*, y*(0) = 0, *y'*(0) = 1

To determine

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

Explanation

**Given data:**

The differential equation is,

with

Consider the auxiliary equation is,

Roots of equation (2) are,

Write the expression for the complementary solution,

The particular solution

Differentiate equation (3) with respect to *x*,

Differentiate equation (3) with respect to *x*,

Substitute equations (3) and (5) in equation (1),

Differentiate the equation (6) with respect to *x*.

Simplify the equation.

Substitute 0 for *x* in equation (6),

Substitute
*x* in equation (6),

Substitute
*A* in equation (8)

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