常微分方程初等解法及其求解技巧畢業(yè)論文(已修改)
2025-07-09 14:53 本頁面
【正文】 目 錄摘 要 ...............................................................I關(guān)鍵詞 ..............................................................IAbstract .............................................................IKey words ...........................................................I 言 .............................................................1 ..............................................1 常微分方程變量可分離類型解法 ...................................1 直接可分離變量的微分方程 ....................................2 可化為變量分離方程 ..........................................2 常數(shù)變易法 .....................................................9 一階線性非齊次微分方程的常數(shù)變易法 ..........................9 一階非線性微分方程的 常數(shù)變易法 .............................10 積分因子法 ....................................................16 .............................17 幾個重要的變換技巧及實例 ......................................18 變 為 .................................................18dxy 分項組合法組合原則 .........................................19 積分因子選擇 ...............................................20參考文獻 ...........................................................21致 謝 .............................................................22I常微分方程初等解法及其求解技巧摘 要常微分方程是微積分學(xué)的重要組成部分，的問題，常常通過變量分離、兩邊積分，如果是高 階 的則通過適當(dāng)?shù)淖兞看鷵Q，達到降 結(jié)：先介紹求解常微分方程的幾種初等解法，如變量分離法，常數(shù)變易法， 積分因子法等，在學(xué)習(xí)過程中，通過對不同 類型的方程求解，方程求解中的變換技巧及規(guī)律，并通過實例來分析這幾類方法之間的聯(lián)系及優(yōu)劣，從而能快速的找到最佳解法.關(guān)鍵詞變量分離法 常數(shù)變易法 積分因子 變換技巧Elementary Solution and Solving Skills of Ordinary Differential EquationAbstractOrdinary differential equations are important ponents of calculus and used extensively for the studies on specific issues. Ordinary differential equations are often resolved by the means of variable separation and both sides integral. If they are higherorder ones, we can reduce their order by proper variable substitution to solve this problem. This essay aims at concluding systematically the methods of different types of differential equations and its resoling skills. First of all, I’d would like to introduce several basic resolutions of differential equations, such as variable separation, constant threats, points factor, etc. In the process of learning, I’d like to reduce the law of resolving ordinary differential equations by resolving different types of equations. Then, we describe several equations resolutions and for transformation techniques and its laws, and we also analyze the advantages and disadvantages and connections by using the examples of these methods to be able to find the best solution quickly.Key wordsVariable separation。 constant threats。 points factor。 transform techniques1 言數(shù)學(xué)發(fā)展的歷史告訴我們，300 年來數(shù)學(xué)分析是數(shù)學(xué)的首要分支，而微分方程又是數(shù)學(xué)分析的心臟，常微分方程從它產(chǎn)生的那天起, 就是研究自然界變化規(guī)律、研究人類社會結(jié)構(gòu)、生態(tài)結(jié)構(gòu)和工程技術(shù).現(xiàn)在，常微分方程在很多學(xué)科領(lǐng)域內(nèi)有著重要的應(yīng)用，自動控制、各種 電子學(xué)裝置的設(shè)計、 彈道的計算、飛機和
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