general solution: meaning, definition, pronunciation and examples
C1-C2 (Technical)Formal, Academic, Technical
Quick answer
What does “general solution” mean?
A complete answer or formula that includes all possible specific solutions or cases to a problem, particularly in mathematics.
Audio
Pronunciation
Definition
Meaning and Definition
A complete answer or formula that includes all possible specific solutions or cases to a problem, particularly in mathematics.
A broad, overarching answer or approach intended to address all aspects of a problem or situation, often found in scientific, philosophical, or strategic contexts.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. The term is identical in form and function across both varieties.
Connotations
In academic contexts, it carries the same precise, technical meaning. In general use, it may be perceived as slightly more formal or high-register.
Frequency
Equally frequent in technical/scientific writing in both varieties. Rare in casual conversation.
Grammar
How to Use “general solution” in a Sentence
the general solution to [NOUN PHRASE]the general solution of [NOUN PHRASE]a general solution for [NOUN PHRASE]Vocabulary
Collocations
Usage
Meaning in Context
Business
Used rhetorically to propose a strategy or policy meant to address a wide range of issues, e.g., 'We need a general solution to our supply chain vulnerabilities.'
Academic
The standard, precise term in mathematics and engineering for a solution containing arbitrary constants or parameters.
Everyday
Rare. If used, it means 'an answer that works for everything,' often with scepticism, e.g., 'There's no general solution for raising teenagers.'
Technical
The primary domain. Refers to the family of all possible solutions to a differential equation, optimization problem, or logical system.
Vocabulary
Synonyms of “general solution”
Strong
Neutral
Weak
Vocabulary
Antonyms of “general solution”
Watch out
Common Mistakes When Using “general solution”
- Using 'generic solution' interchangeably (a 'generic solution' implies typicality, not completeness). Using 'general solution' for a vague or non-specific idea rather than a complete, parametric one. Incorrect preposition: 'general solution of the problem' is more common than 'general solution for the problem' in maths.
FAQ
Frequently Asked Questions
Not exactly. In technical fields (maths, physics), 'general solution' is a precise term for a parametric family of solutions. 'Universal solution' is more common in everyday language for a one-size-fits-all fix and lacks the technical precision.
Yes, you can have 'a general solution' (singular) or 'general solutions' (plural), e.g., 'We explored several general solutions before selecting the most efficient one.'
The direct opposite is a 'particular solution' or 'specific solution'—a single solution obtained by assigning specific values to the arbitrary constants in the general solution.
No, it is primarily an academic and technical term. In everyday talk, people are more likely to say 'an overall answer' or 'a fix for everything'.
A complete answer or formula that includes all possible specific solutions or cases to a problem, particularly in mathematics.
General solution is usually formal, academic, technical in register.
General solution: in British English it is pronounced /ˈdʒen.rəl səˈluː.ʃən/, and in American English it is pronounced /ˈdʒen.rəl səˈluː.ʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “a silver bullet (metaphorical parallel in non-technical contexts)”
Learning
Memory Aids
Mnemonic
Think of a **general** in an army who commands ALL the specific troops. The **general solution** commands or contains ALL the specific possible answers.
Conceptual Metaphor
A CONTAINER (holding all specific instances), a MAP (showing all possible routes), a FORMULA (generating all outcomes).
Practice
Quiz
In which context is 'general solution' used with its most precise technical meaning?