佳木斯职业学院学报
佳木斯職業學院學報
가목사직업학원학보
Journal of Juamjusi Education Institute
2015年
10期
286-288
,共3页
微分方程%积分因子%恰当微分方程%一阶微分
微分方程%積分因子%恰噹微分方程%一階微分
미분방정%적분인자%흡당미분방정%일계미분
Differential equation%integral factor%appropriate differential equation%first-order differential
微分方程是表达自然规律的一种自然的数学语言。它从生产实践与科学技术中产生,而又成为现代科学技术中分析问题与解决问题的一个强有力的工具。人们在探求物质世界某些规律的过程中,一般很难完全依靠实验观测认识到该规律,反而是依照某种规律存在的联系常常容易被我们捕捉到,而这种规律用数学语言表达出来,其结果往往形成一个微分方程,而一旦求出方程的解,其规律则一目了然。对于恰当微分方程我们有一个通用的求解公式。但是,就如大家都知道的那样,并不是所有的微分形式的一阶方程都是恰当微分方程。对于这类不是恰当微分方程的一阶常微分方程该如何求出它的解呢,这就需要用到这里我们讨论的积分因子了。
微分方程是錶達自然規律的一種自然的數學語言。它從生產實踐與科學技術中產生,而又成為現代科學技術中分析問題與解決問題的一箇彊有力的工具。人們在探求物質世界某些規律的過程中,一般很難完全依靠實驗觀測認識到該規律,反而是依照某種規律存在的聯繫常常容易被我們捕捉到,而這種規律用數學語言錶達齣來,其結果往往形成一箇微分方程,而一旦求齣方程的解,其規律則一目瞭然。對于恰噹微分方程我們有一箇通用的求解公式。但是,就如大傢都知道的那樣,併不是所有的微分形式的一階方程都是恰噹微分方程。對于這類不是恰噹微分方程的一階常微分方程該如何求齣它的解呢,這就需要用到這裏我們討論的積分因子瞭。
미분방정시표체자연규률적일충자연적수학어언。타종생산실천여과학기술중산생,이우성위현대과학기술중분석문제여해결문제적일개강유력적공구。인문재탐구물질세계모사규률적과정중,일반흔난완전의고실험관측인식도해규률,반이시의조모충규률존재적련계상상용역피아문포착도,이저충규률용수학어언표체출래,기결과왕왕형성일개미분방정,이일단구출방정적해,기규률칙일목료연。대우흡당미분방정아문유일개통용적구해공식。단시,취여대가도지도적나양,병불시소유적미분형식적일계방정도시흡당미분방정。대우저류불시흡당미분방정적일계상미분방정해여하구출타적해니,저취수요용도저리아문토론적적분인자료。
Differential expression of natural law is a natural mathematical language. It is from the production practice and science and technology generation, but modern science and technology in analyzing and solving problems in a powerful tool. Some people in the law to explore the process of the material world, the genera experimental observation is difficult to completely rely on recognizing that the law, but there is a link in accordance with certain laws are often easy to catch us, and such laws expressed in mathematical language, which often results in the formation of a differential equation, and once obtained equation, the law is clear So we must be able to find its solution. Meanwhile, for the appropriate differential equation we have a general formula to solve. However, as we al know, not al forms of first-order differential equations are appropriate differential equation. For these are not appropriate differential equation differential equation, how it obtained its solution, which we are discussing here need to use the integrating factor.