V2EX general-solution

General Solution

释义 Definition

(数学)通解:指满足某个方程(尤其是微分方程)或问题的所有解的表达式,通常包含一个或多个任意常数/参数;由此可通过给定初始条件或边界条件得到特解。(在更广义语境中也可指“普遍适用的解决方案”。)

发音 Pronunciation (IPA)

/denrl slun/

例句 Examples

The general solution includes an arbitrary constant.
通解包含一个任意常数。

After solving the differential equation, we obtained the general solution, and then used the initial condition to find a particular solution.
解出该微分方程后,我们得到了通解,然后用初始条件求出特解。

词源 Etymology

general 来自拉丁语 generalis,意为“普遍的、总体的”;solution 来自拉丁语 solutio(“解开、解除”)。合起来 general solution 字面即“总体的解”,在数学中引申为“包含所有可能情形的解的形式”。

相关词 Related Words

文学与经典著作 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. L. Ince)
  • Introduction to Ordinary Differential Equations(Shepley L. Ross)
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