# Find the particular solution of the differential equation dydx + ycos(x) = 6cos(x) satisfying the...

## Question:

Find the particular solution of the differential equation dydx + ycos(x) = 6cos(x) satisfying the initial condition y(0) = 8.

## First Order Differential Equation:

A differential equation relates a function with its derivative, which is the instantaneous rate of change of the function. There are several techniques to solve a differential equation. In this problem, we'll use the integrating factor.

If a first-order differential equation is of the form: {eq}\displaystyle \frac{dy}{dx}+ P(x) y = Q(x) {/eq}

The integrating factor {eq}\mu= e^{\int P(x) \ dx} {/eq}

Next, we'll compute the given condition to get the desired solution.

## Answer and Explanation:

We are given: {eq}\displaystyle \frac{dy}{dx}+ ycos(x) = 6cos(x) {/eq}

Integrating facor {eq}\mu {/eq}:

{eq}\displaystyle \mu = e^{6 cos(x) \...

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Differential Calculus: Definition & Applications

from Calculus: Help and Review

Chapter 13 / Lesson 6
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