---
tag: 07DJAZW32T
kind: concept
name: Integrating factor
msc: [34A05]
sources:
  - url: https://en.wikipedia.org/wiki/Integrating_factor
    locator: lead section
same_as:
  wikidata: Q2734005
  wikipedia: Integrating factor
---

## Summary

An integrating factor is a function by which one multiplies a differential equation so that it can be integrated directly.
For the linear equation $y' + p y = q$, the factor $e^{\int p}$ turns the left side into the derivative $\left(e^{\int p} y\right)'$. See the [[definition|01THH3Y3YP]].