Chapter 17.2, Problem 2E

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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.

**2.** *y"* – 3*y'* = sin 2*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 for two real roots,

Substitute 0 for

The Right hand side (RHS) of a differential equation contains only sine function. The particular solution for this case can be expressed as follows.

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

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

Substitute equations (5) and (6) in (1),

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

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