# Find the general solution of the linear ODE y prime + y = sqrt(x) e^(-x).

## Question:

Find the general solution of the linear ODE {eq}\; {y}' + y = \sqrt{x} \, e^{-x} {/eq}.

## First Order Linear Differential Equations

These are the differential equation in the form

{eq}y' + P(x)y = Q(x) {/eq}

This is solved by getting an integration factor through the equation:

{eq}I = e^{\int P(x)\;dx} {/eq}

This is multiplied to the differential equation, then integrate the whole equation to solve.

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The given differential equation

{eq}\; {y}' + y = \sqrt{x} \, e^{-x} {/eq}

is in the first order linear differential equation

{eq}y' + P(x)y =... First-Order Linear Differential Equations

from

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.