一类二阶变系数线性微分方程的新解法  

New Method on Solving a kind of Second-order Linear Differential Equations With Variable Coefficients

作　　者：张道祥[1] 李亭亭[1] Zhang Daoxiang;Li Tingting(School of Mathematics and Computer Science, Anhui Normal University, Wuhu Anhui, 241002, China)

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241002

出　　处：《科技资讯》2017年第20期207-208,共2页Science & Technology Information

摘　　要：二阶线性微分方程在常微分方程理论中占有重要地位.求解常系数线性微分方程的方法有特征根法、比较系数法、拉普拉斯变换法等,但二阶变系数线性微分方程却没有一般的方法进行求解。该文通过使用变量代换将一般的二阶变系数齐次线性微分方程化为方程来进行求解,给出了其具有通解的一个充分条件。同时,举例说明了该方法的应用。The second order linear differential equation plays an important role in the theory of ordinary differential equations.There have several methods on solving second order linear differential equation with constant coefficients,such as eigenvaluemethod,comparative coefficient method,Laplace transform method.While it has no normal method to solve second order lineardifferential equation with variable coefficients.By using the variable substitution method,the general solutions of secondorderlinear differential equations with variable coefficients are obtained.Moreover,two examples are given to illustrate theresults.

关 键 词：二阶变系数线性微分方程 通解 方程 

分 类 号：O175.1[理学—数学]