---
tag: 0SWTJ5VC07
kind: concept
name: Linear equation with constant coefficients
msc: [34A30]
sources:
  - url: https://en.wikipedia.org/wiki/Linear_differential_equation
    locator: Homogeneous equation with constant coefficients
---

## Summary

A linear equation with constant coefficients is a linear differential equation $y^{(n)} + a_{n-1} y^{(n-1)} + \dots + a_0 y = b(x)$ with real constants $a_0, \dots, a_{n-1}$.
The roots of its characteristic polynomial give all solutions of the homogeneous equation. See the [[definition|0A6PGTTP2A]].