---
tag: 0GZWXM2DKE
kind: concept
name: Characteristic equation
msc: [34A30]
sources:
  - url: https://en.wikipedia.org/wiki/Characteristic_equation_(calculus)
    locator: lead section
same_as:
  wikidata: Q1062971
  wikipedia: Characteristic equation (calculus)
---

## Summary

The characteristic equation of a homogeneous linear differential equation with constant coefficients is the polynomial equation obtained from the trial solution $e^{r x}$.
Its roots determine the solutions of the differential equation. See the [[definition|0QDXMG46QW]].