---
tag: 0RN88KZBJ3
kind: concept
name: Homogeneous first-order equation
msc: [34A05]
sources:
  - url: https://en.wikipedia.org/wiki/Homogeneous_differential_equation
    locator: lead section
---

## Summary

A homogeneous first-order equation is an equation $y' = F(y/x)$, in which the slope depends only on the ratio $y/x$.
The substitution $y = x v$ changes it into a separable equation. See the [[definition|0K4ZWTFSV5]].