---
tag: 01J7FZ65J0
kind: concept
name: Maximal solution
msc: [34A12]
sources:
  - url: https://en.wikipedia.org/wiki/Ordinary_differential_equation
    locator: Global uniqueness and maximum domain of solution
---

## Summary

A maximal solution of an ordinary differential equation is a solution that is not the restriction of a solution on a larger interval.
Under a local Lipschitz condition, each initial value problem has exactly one maximal solution. See the [[definition|019VSXSFMQ]].