# \frac{dy}{dt} - \frac{1}{2}y = e^\frac{1}{2}t \sin t

## Question:

{eq}\frac{dy}{dt} - \frac{1}{2}y = e^\frac{1}{2}t \sin t {/eq}

## Solution to Differential Equation:

Differential equation with form {eq}\displaystyle \frac{dy}{dt}+Py=Q {/eq} is called linear differential equation.

Here, P and Q are constants or function of t only.

It's solution will be,

{eq}\displaystyle \:y\left(I.F\right)=\int \:Q\left(I.F\right)dt+C {/eq} with {eq}\displaystyle I.F=e^{\int \:P\:dt} {/eq}

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Given differential equation is

{eq}\displaystyle \frac{dy}{dt} - \frac{1}{2}y = e^\frac{1}{2}t \sin t {/eq}

which is linear differential equation

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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.