V2EX particular solution

Particular Solution

释义 Definition

(数学/微分方程)特解:在满足某个方程(常见于微分方程或线性方程)的所有解中,满足给定初始条件/边界条件的那一个具体解。常与 general solution(通解) 相对。(在微分方程中也常指“非齐次方程的一个特定解”,用于与齐次解相加得到通解。)

发音 Pronunciation (IPA)

/ptkjlr slun/

例句 Examples

The particular solution satisfies the initial condition.
特解满足初始条件。

After finding the homogeneous solution, we add a particular solution to obtain the general solution of the nonhomogeneous equation.
在求出齐次解之后,我们再加上一个特解,从而得到非齐次方程的通解。

词源 Etymology

particular 源自拉丁语 particula(“小部分、细节”),引申为“具体的、特定的”;solution 源自拉丁语 solutio(“解开、解除”),在数学语境中发展为“方程的解”。合起来 particular solution 就是“某个特定条件下的具体解/特定解”。

相关词 Related Words

文学与作品 Literary Works

  • Elementary Differential Equations and Boundary Value Problems(Boyce & DiPrima)
  • Differential Equations with Applications and Historical Notes(George F. Simmons)
  • Ordinary Differential Equations(E. A. Coddington)
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