Differential Equation
An equation relating a function with one or more of its derivatives.
Also: ODE · PDE
Definition
A differential equation is a mathematical equation that relates a function to its derivatives, expressing how a quantity changes with respect to one or more variables. Ordinary differential equations (ODEs) involve functions of a single variable, while partial differential equations (PDEs) involve functions of multiple variables. They are the primary mathematical language for modeling physical systems such as population growth, heat conduction, and electromagnetic fields.
Example
“The spread of an infectious disease is modeled by the SIR differential equations, which track how the rates of change of susceptible, infected, and recovered populations depend on current case numbers, helping epidemiologists predict outbreak trajectories.”
Synonyms
- ODE
- PDE
- rate equation
- dynamical equation
Images
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Related Terms
- Integration
- Calculus
- Laplace Transform
- Boundary Value Problem