# Use variation of parameters method to find a particular solution for the differential equation ...

## Question:

Use variation of parameters method to find a particular solution for the differential equation

{eq}y'' - 9y = \frac{9x}{e^{3x}}. {/eq}

## Variation Of Parameter Method:

Consider the differential equation {eq}\displaystyle y"+q(t)y'+r(t)y=g(t) {/eq}

assume that {eq}\displaystyle y_1(t) ,y_2(t) {/eq} are a fundamental set of solutions for {eq}\displaystyle y"+q(t)y'+r(t)y=0 {/eq}

Then a particular solution to the non-homogeneous differential equation is

{eq}\displaystyle Y_p(t)=-y_1\int\frac{y_2g(t)}{W(y_1,y_2)} +y_2\int\frac{y_1g(t)}{W(y_1,y_2)} {/eq}

## Answer and Explanation:

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View this answerGiven differential equation

{eq}\displaystyle...

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Chapter 16 / Lesson 3In 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.