Chapter 17.2, Problem 17E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.

**17.** *y"* + 2*y' +* 10*y* = *x*^{2}*e ^{-x}* cos 3

To determine

**To write:** The trail solution for 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 the complex roots,

Substitute

Since

If Right hand side (RHS) of a differential equation contains a product of an exponential function, a cosine function, and *n*^{th} order polynomial, the trail solution of the differential equation also should be a product of these corresponding choices. So, the trail solution

Here,

*n* is the order of a polynomial, and

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