# Solve differential equation: {eq}y' + y = \sin(x) {/eq}

## Question:

Solve differential equation:

{eq}y' + y = \sin(x) {/eq}

## Integrating Factor

The integrating factor is applied to a first order linear differential equation so the equation becomes easier to integrate. For a function in the form {eq}y' + p(x)y = q(x) {/eq}, the integrating factor is given by {eq}I = e^{\int p(x)\,dx} {/eq}.

## Answer and Explanation:

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The given differential equation has the following form.

\begin{align} y' + p(x)y &= q(x) \\ y' + y &= \sin(x) \\ \text{where } p(x) &= 1,...

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