Chapter 17.2, Problem 19E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.

**19.** 4*y"* + *y* = cos *x*

(a)

To determine

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

Explanation

**Given data:**

The differential equation is,

Consider the auxiliary equation.

Roots of equation (2) are,

Write the expression for the complementary solution of two complex roots

Substitute 0 for

If Right hand side (RHS) of a differential equation contains only cosine function, Therefore, the trail solution

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

Differentiate equation (6) with respect to *x*,

(b)

To determine

**To solve:** The differential equation by using method of variation of parameters.

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