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Use the method of undetermined coefficients to find a particular solution of the following...

Question:

Use the method of undetermined coefficients to find a particular solution of the following differential equations, and then find the general solution.

a. {eq}y" - y' + y = e^{2x} {/eq}

b. {eq}y'' - 5y' + 6y = \left ( 2x - 3 \right )e^x {/eq}

Undetermined Coefficients Method:

The undetermined coefficients method proposes a particular solution for the non-homogeneous differential equation with constant coefficients.

{eq}ay'' + by' + cy = g(x) {/eq} when {eq}g(x) {/eq} has a special form, involving only polynomials, exponentials, sines and cosines, or g(x) is a finite linear combination of this functions.

Answer and Explanation:

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a. {eq}y" - y' + y = e^{2x} {/eq}

We must calculate the solution of the associated homogeneous equation, to verify that the function...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.


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