Glossary · Research and quantitative methods
Ordinary differential equation (ODE)
An equation relating a function of one independent variable to one or more of that function's derivatives.
Also called: ODE, ordinary differential equations, ODEs
Definition
An ordinary differential equation describes how a quantity changes with respect to a single independent variable, often time. ODEs can represent one quantity or a coupled system, and their behavior may be studied analytically, numerically, or geometrically through vector fields and phase portraits.
Why it matters
ODE models connect explicit assumptions about change to trajectories that can be calculated, compared with observations, and tested for sensitivity or failure.
Common misunderstanding
A mathematically valid ODE solution does not prove that the chosen variables, parameters, initial conditions, or model assumptions represent the real system adequately.
Related terms
Related system family: Measurement & Search Signals
Sources
- Differential Equations (opens in a new tab) · MIT OpenCourseWare
Last reviewed July 16, 2026