常微分方程初等解法及其求解技巧畢業(yè)論文-在線瀏覽
2024-08-07 14:53本頁面
【正文】 微分方程幾類初等解法之間的聯(lián)系及優(yōu)劣，從而能快速的找到最優(yōu)解法.下面以例題來介紹“ 變換”的技巧和規(guī)律. 變 為dxy若微分方程為（或可轉(zhuǎn)換為）,??yxgfd?當(dāng) 較 簡單時(shí)，可 變變 為 ，此 時(shí) 方程變?yōu)??yxfg,f,19,??yxfgd?經(jīng)此變換后方程可能是前面所介紹的某類方程.例 求方程 的通解yxd??2解 令 ， ，因此原方程不屬于前面所介紹的各類方程，??f,??yxg2,但 ，??xyxf21,??所以，xyd?方程屬于伯努利方程. 令 ， ，方程變?yōu)?.2xz?39。 points factor。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(gè)重要的變換技巧及實(shí)例 ......................................18 變 為 .................................................18dxy 分項(xiàng)組合法組合原則 .........................................19 積分因子選擇 ...............................................20參考文獻(xiàn) ...........................................................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(dá)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(shí)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
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