differential equation: meaning, definition, pronunciation and examples
C1/C2technical/academic
Quick answer
What does “differential equation” mean?
An equation that relates a function with its derivatives, expressing how a quantity changes relative to other quantities.
Audio
Pronunciation
Definition
Meaning and Definition
An equation that relates a function with its derivatives, expressing how a quantity changes relative to other quantities.
A mathematical model used to describe dynamic systems in physics, engineering, biology, economics, and other sciences, where the rate of change of a variable is linked to its current state and/or other variables.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences; conceptual terminology identical.
Connotations
Strongly associated with advanced mathematics, physics, and engineering curricula in both regions.
Frequency
Equally common in academic and technical contexts in both UK and US English.
Grammar
How to Use “differential equation” in a Sentence
The differential equation describes/governs/models...Solving the differential equation yields...We derive/formulate a differential equation for...Vocabulary
Collocations
Examples
Examples of “differential equation” in a Sentence
verb
British English
- The process is differentialled to obtain the governing equation.
- We need to differentialise the relationship.
American English
- The relationship is differentiated to yield the model equation.
- We must differentiate to formulate the core equation.
adverb
British English
- The system behaves differential-equation-wise.
- It was modelled differential-equation-ly.
American English
- The phenomenon is described differentially via an equation.
- It is formulated in a differential-equation manner.
adjective
British English
- The differential equation approach is fundamental.
- This is a differential-equation-based model.
American English
- The differential equation framework is standard.
- We use a differential equation formulation.
Usage
Meaning in Context
Business
Rare, except in quantitative finance or econometric modelling.
Academic
Core concept in mathematics, physics, engineering, and applied sciences.
Everyday
Virtually never used in casual conversation.
Technical
Fundamental term in modelling dynamical systems across disciplines.
Vocabulary
Synonyms of “differential equation”
Strong
Neutral
Weak
Vocabulary
Antonyms of “differential equation”
Watch out
Common Mistakes When Using “differential equation”
- Using 'differential' as a noun alone to mean 'differential equation' (e.g., 'I solved the differential' is incorrect).
- Confusing 'differential equation' with 'difference equation' (which involves discrete steps, not infinitesimal calculus).
FAQ
Frequently Asked Questions
An ordinary differential equation (ODE) involves a function of a single independent variable and its derivatives. A partial differential equation (PDE) involves a function of multiple independent variables and its partial derivatives with respect to those variables.
No, they are ubiquitous in science and engineering. They are used in biology (population dynamics, epidemiology), chemistry (reaction kinetics), economics (economic growth models), engineering (control theory, heat transfer), and finance (option pricing).
Solving a differential equation means finding the function (or family of functions) that satisfies the equation. This can involve finding an explicit formula (analytic solution) or approximating the function's values using numerical methods.
It is a countable noun. You can have 'a differential equation', 'two differential equations', or 'many differential equations'.
An equation that relates a function with its derivatives, expressing how a quantity changes relative to other quantities.
Differential equation is usually technical/academic in register.
Differential equation: in British English it is pronounced /ˌdɪf.əˌren.ʃəl ɪˈkweɪ.ʒən/, and in American English it is pronounced /ˌdɪf.əˌren.ʃəl ɪˈkweɪ.ʒən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “Not applicable; technical term without idiomatic use.”
Learning
Memory Aids
Mnemonic
Differential = about differences (rates of change); Equation = a statement of equality. So, it's an equation that balances a quantity with how it changes.
Conceptual Metaphor
A 'recipe for change' – given the current state and the rules of change (the equation), you can predict future behaviour.
Practice
Quiz
Which of the following is a differential equation?