Find the general solution of the differential equation y' + 2y = 4\cos 2x; y(\pi/4) = 3

Question:

Find the general solution of the differential equation {eq}y' + 2y = 4\cos 2x; y(\pi/4) = 3 {/eq}

First order Linear differential equation:

We write the given first order linear differential equation in the standard form {eq}y'+p(x)y = q(x) {/eq}

We calculate the integrating factor {eq}e^{\int p(x) dx} {/eq}

Further, we multiply the integrating factor to both sides of the differential equation and then we integrate both the sides separately to get the solution.

Answer and Explanation: 1

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The given first order linear differential equation can be rewritten as {eq}y'+2y=4\cos 2x; y(\frac{\pi}{4}) = 3 {/eq}

The integrating factor is...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In 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.


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