# Consider the differential equation 16y" + y = sec(x/4) tan(x/4) Find the general solution of the...

## Question:

Consider the differential equation:

{eq}16'' + y = sec(\frac{x}{4}) tan(\frac{x}{4}) {/eq}

Find the general solution of the related homogeneous differential equation. Find the general solution of the nonhomogeneous differential equation.

## General Solution:

We have to find the general solution of the second-order differential equation.

For finding the general solution of the equation of the form {eq}ay''+by'+cy=g(x) {/eq}, first, we calculate the general solution of the homogenous equation and then we calculate the particular solution of the non-homogeneous equation and lastly we combine both the results.

## Answer and Explanation: 1

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Given

{eq}16y'' + y = sec(\frac{x}{4}) tan(\frac{x}{4}) \\ y''+\dfrac{1}{16}y''=\dfrac{1}{16}sec(\frac{x}{4}) tan(\frac{x}{4}) {/eq}

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Chapter 19 / Lesson 10What is the constant of Variation? Learn the definition for the constant of variation. Discover how the constant of variation "K" is used to determine the change in "Y" based on the change in "X"

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