用“升阶法”求解一类一阶线性微分方程——兼谈逆向思维能力的培养  

Solving a Class of First Order Linear differential Equations by “Ascending Order Method”——Talking about the Cultivation of Reverse Thinking Ability

作　　者：吴建强[1] 

机构地区：[1]广东工业大学华立学院,广东广州511325

出　　处：《高等数学研究》2016年第3期26-28,共3页Studies in College Mathematics

基　　金：广东省高等数学精品资源共享课立项项目(2013)

摘　　要："升阶法"能够把一类特殊的一阶线性微分方程化为二阶常系数齐次线性微分方程求解,而一般的一阶线性微分方程的求解问题可以转化为二元函数全微分的求积问题.利用"升阶法"和"全微分法"对学生进行逆向思维训练,培养学生的创新思维能力.＂Ascending order method＂ can put a special fist-order linear differential equation into second order constant coefficient homogeneous linear differential equation for general solution, and the solving problem of first- order linear differential equation can be transformed into the integral of total differential of two variable function. The students can be trained in reverse and their creative thinking ability can thinking by using the method of ascending order and full differential method, therefore be developed.

关 键 词：一阶线性微分方程 升阶法 全微分法 逆向思维 

分 类 号：O175.1[理学—数学]