---
tag: 037ZNY7NAG
kind: concept
name: System of linear differential equations
msc: [34A30]
sources:
  - url: https://en.wikipedia.org/wiki/Matrix_differential_equation
    locator: lead section
same_as:
  wikidata: Q6787870
  wikipedia: Matrix differential equation
---

## Summary

A system of linear differential equations is an equation $x' = A(t) x + b(t)$ for a vector-valued function $x$, with a matrix $A(t)$ of coefficients.
Its theory extends that of a single linear equation. See the [[definition|0A6QZ367GX]].