clairaut equation: meaning, definition, pronunciation and examples
Very Low (Technical)Highly Technical / Academic (Mathematics)
Quick answer
What does “clairaut equation” mean?
A type of first-order ordinary differential equation of the form y = xy′ + f(y′), named after the French mathematician Alexis Clairaut.
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Pronunciation
Definition
Meaning and Definition
A type of first-order ordinary differential equation of the form y = xy′ + f(y′), named after the French mathematician Alexis Clairaut.
A differential equation whose general solution is a family of straight lines, but which may also have a singular solution (an envelope) that is not a member of this family. It is a standard example in the study of singular solutions and envelopes of families of curves.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning, spelling, or usage. The name 'Clairaut' is pronounced with a French origin in both dialects.
Connotations
Purely mathematical, with no cultural or regional connotations.
Frequency
Identically rare and specialised in both varieties.
Grammar
How to Use “clairaut equation” in a Sentence
The Clairaut equation [verb: is, has, yields]...Vocabulary
Collocations
Examples
Examples of “clairaut equation” in a Sentence
adjective
British English
- A Clairaut-type formulation was used.
- The problem exhibited Clairaut characteristics.
American English
- It's a Clairaut-form differential equation.
- We need a Clairaut-equation approach.
Usage
Meaning in Context
Business
Never used.
Academic
Used exclusively in advanced mathematics textbooks, papers, and lectures on differential equations.
Everyday
Never used.
Technical
The primary context of use.
Vocabulary
Synonyms of “clairaut equation”
Weak
Watch out
Common Mistakes When Using “clairaut equation”
- Misspelling as 'Clairaut', 'Clairaud', or 'Clairout'.
- Incorrectly classifying it as a second-order equation.
- Forgetting to look for the singular solution (envelope) after finding the general solution.
FAQ
Frequently Asked Questions
It is named after the French mathematician, astronomer, and geophysicist Alexis Claude Clairaut (1713–1765).
It is generally nonlinear because of the function f(y′), unless f is a linear function.
The singular solution represents an envelope of the family of straight lines from the general solution and is often a physically or geometrically meaningful curve not obtainable by choosing a constant in the general solution.
Primarily in pure mathematics within the study of differential equations. It serves as a canonical example for teaching the concepts of singular solutions and envelopes. It has limited direct application in specific geometrical or physical problems.
A type of first-order ordinary differential equation of the form y = xy′ + f(y′), named after the French mathematician Alexis Clairaut.
Clairaut equation is usually highly technical / academic (mathematics) in register.
Clairaut equation: in British English it is pronounced /ˌkleɪˈrəʊ ɪˈkweɪʒ(ə)n/, and in American English it is pronounced /ˌkleɪˈroʊ ɪˈkweɪʒən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think: 'CLAIm the ROUTh' – Clairaut equations claim a route (y = x * slope + function(slope)) to find singular solutions.
Conceptual Metaphor
A puzzle where the general answer is a family of straight paths, but the special, hidden answer is a curved envelope touching them all.
Practice
Quiz
What is a defining feature of a Clairaut equation?