Chapter 17.2, Problem 4E

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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.

**4.** *y"* – 2*y'* + 2y = *x* + *e ^{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 the complex roots,

Substitute

Since

If Right hand side (RHS) of a differential equation contains an addition of an exponential function and 1^{st} order polynomial. So, the particular solution

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