---
tag: 07VX34QXAV
kind: concept
name: Solution of an ordinary differential equation
aliases: [integral-curve]
msc: [34A99]
sources:
  - url: https://en.wikipedia.org/wiki/Integral_curve
    locator: lead section
same_as:
  wikidata: Q1665406
  wikipedia: Integral curve
---

## Summary

A solution of an [[ordinary differential equation|0NT64JV96A]] is a function on an interval that satisfies the equation at each point.
For a first-order system given by a vector field, the solutions are the integral curves. These are the curves whose velocity is the value of the vector field at each point.
See the [[definition|04SW7WECS8]].