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Find the indicated particular solution of the differential equation. y' + 2y*cot(x) = 4cos(x); x...

Question:

Find the indicated particular solution of the differential equation.

y' + 2y*cot(x) = 4cos(x); x = π/2 when y = 1/3.

The Solution of Linear Differential Equation

The general form for Linear Differential Equation(L.D.E) for any given function f(x) is as follows

{eq}\begin{align*} \Rightarrow &y' + p(x) \cdot y = q(x) \end{align*} {/eq}

where p(x) and q(x) are constant or function of x.

The integrating factor {eq}\mu(x) {/eq} for the L.D.E will be

{eq}\begin{align*} \Rightarrow &\mu (x) = e^{\int p(x) \ dx} \end{align*} {/eq}

The solution for the L.D.E will be as follows

{eq}\begin{align*} \Rightarrow &y \cdot \mu(x) = \int \mu(x) \cdot q(x) \ dx \end{align*} {/eq}

Answer and Explanation: 1

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Given, the differential equation

{eq}\begin{align*} y' + 2y*cot(x) = 4cos(x) \end{align*} {/eq}

The given D.E is Linear Differential Equation,

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Integrating Factor: Method & Example

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Chapter 12 / Lesson 6
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Learn how to find integrating factors. Review the integrating factor method and formula to solve linear first- and second-order differential equations with examples.


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