particular solution: meaning, definition, pronunciation and examples
LowTechnical/Academic
Quick answer
What does “particular solution” mean?
A specific solution to a differential equation that satisfies both the equation and given initial or boundary conditions.
Audio
Pronunciation
Definition
Meaning and Definition
A specific solution to a differential equation that satisfies both the equation and given initial or boundary conditions.
In mathematics, a solution that fits a specific set of constraints, as opposed to the general solution which contains arbitrary constants. In broader contexts, it can metaphorically refer to a solution tailored to a specific problem rather than a universal one.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling of related words may differ (e.g., 'initialise' vs. 'initialize').
Connotations
Identical technical connotations in both varieties.
Frequency
Equally low frequency in both varieties, confined to technical contexts.
Grammar
How to Use “particular solution” in a Sentence
particular solution to [equation]particular solution for [condition]particular solution of [system]Vocabulary
Collocations
Examples
Examples of “particular solution” in a Sentence
verb
British English
- We need to particularise the solution for these initial values.
- The method involves particularising the general integral.
American English
- We need to particularize the solution for these initial values.
- The method involves particularizing the general integral.
adverb
British English
- The function behaves particularly well at the boundary.
- The solution is particularly suited to this case.
American English
- The function behaves particularly well at the boundary.
- The solution is particularly suited to this case.
adjective
British English
- The particular integral is a key component.
- We found a particular integral satisfying the conditions.
American English
- The particular integral is a key component.
- We found a particular integral satisfying the conditions.
Usage
Meaning in Context
Business
Rarely used; if used, it would be metaphorical, e.g., 'We need a particular solution for this client's unique problem.'
Academic
Primary context. Used in mathematics, engineering, and physics lectures and textbooks.
Everyday
Virtually never used in everyday conversation.
Technical
Standard term in differential equations, control theory, and mathematical modelling.
Vocabulary
Synonyms of “particular solution”
Strong
Neutral
Weak
Vocabulary
Antonyms of “particular solution”
Watch out
Common Mistakes When Using “particular solution”
- Using 'particular solution' to mean 'a very good solution' in non-technical contexts.
- Confusing it with 'general solution' or 'complementary function'.
- Misspelling as 'particulate solution'.
FAQ
Frequently Asked Questions
Overwhelmingly yes. Its primary and almost exclusive use is in mathematics, especially in the context of differential equations and linear systems.
In informal technical discussion, 'specific solution' might be understood, but in formal mathematics, 'particular solution' is the standard and preferred term.
The direct opposite is the 'general solution', which contains arbitrary constants. In the context of linear equations, the 'homogeneous solution' or 'complementary function' is also a related contrasting term.
Methods vary by equation type. Common techniques include the method of undetermined coefficients, variation of parameters, or using an ansatz (educated guess) based on the non-homogeneous part of the equation.
A specific solution to a differential equation that satisfies both the equation and given initial or boundary conditions.
Particular solution is usually technical/academic in register.
Particular solution: in British English it is pronounced /pəˌtɪkjʊlə səˈluːʃən/, and in American English it is pronounced /pərˈtɪkjələr səˈluːʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None”
Learning
Memory Aids
Mnemonic
Think of a 'particular' person at a party—they are specific, not just anyone. A 'particular solution' is the specific one that fits the party's (equation's) special conditions.
Conceptual Metaphor
SOLUTION AS A KEY. The general solution is a master key that fits many locks; the particular solution is the specific key cut for one specific lock.
Practice
Quiz
What is the relationship between a general solution and a particular solution?