# a) Find a particular solution to the non homogeneous differential equation y'' + 9y - \cos (3x)...

## Question:

a) Find a particular solution to the non homogeneous differential equation {eq}y'' + 9y - \cos (3x) + \sin (3x) {/eq}

b) Find the most general solution to the associated homogeneous differential equation.

c) Find the solution to the original non homogeneous differential equation satisfying the initial conditions {eq}y(0) = 7, y'(0) = 2 {/eq}

## Second order linear homogeneous differential equation

First we solve linear homogeneous differential equation and find the complementry solution associated to homogeneous differential equation and the find particular integral associated to non homogeneous differential equation. The genearal solution of differential equation will be sum of complementry solution and particular solution

## Answer and Explanation: 1

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View this answerConsider the differential equation

{eq}y'' + 9y - \cos (3x) + \sin (3x)=0,\quad y(0)=7,y{}'(0)=2{/eq}

Rewrite the differential equation as folllows

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Chapter 16 / Lesson 3Learn to define what a linear differential equation and a first-order linear equationÂ are. Learn how to solve the linear differential equation. See examples.

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