---
tag: 07JH131FVP
kind: concept
name: Linear first-order equation
msc: [34A30]
sources:
  - url: https://en.wikipedia.org/wiki/Linear_differential_equation
    locator: First-order equation with variable coefficients
---

## Summary

A linear first-order equation is an equation $y' + p(x) y = q(x)$ with given functions $p$ and $q$.
It is the simplest [[linear differential equation|0QQRP17Z7S]], and an [[integrating factor|07DJAZW32T]] solves it explicitly. See the [[definition|0Z3YKRQZ48]].