# 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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Consider 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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