---
tag: 03F7N3915D
kind: concept
name: Cauchy–Euler equation
msc: [34A30]
sources:
  - url: https://en.wikipedia.org/wiki/Cauchy%E2%80%93Euler_equation
    locator: lead section
same_as:
  wikidata: Q1196465
  wikipedia: Cauchy–Euler equation
---

## Summary

A Cauchy–Euler equation is a linear equation $\sum_k a_k x^k y^{(k)} = 0$ with constant $a_k$, in which the $k$-th derivative has the factor $x^k$.
It has solutions of the form $x^m$, and the change of variable $x = e^t$ gives constant coefficients. See the [[definition|0WDNRBXX7K]].