Chapter 17.2, Problem 21E

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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.

**21.** *y"* – 2*y'* + *y* = *e*^{2x}

(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 the one real root.

Substitute 1 for *r* in equation (3),

If Right hand side (RHS) of a differential equation contains only an an exponential function, the trail solution of the differential equation is also be exponential function. So, 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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