基于降阶的变量替换法在二阶微分方程求解中的应用  

The Application of Variable Substitution Method Based on Reduced Order in Second Order Differential Equations

作　　者：汪雄良[1] 聂芬 WANG Xiong-liang;NIE Fen(College of Liberal Arts and Science,National University of Defense Technology,Changsha,Hunan 410072,China)

机构地区：[1]国防科技大学文理学院,湖南长沙410072

出　　处：《教育教学论坛》2020年第15期277-278,共2页Education And Teaching Forum

基　　金：国防科技大学本科教育教学研究课题(U2018004)。

摘　　要：探讨变量替换法在二阶常系数非齐次微分方程方程求解中的应用。针对二阶常系数非齐次微分方程,直接将二阶常系数线性非齐次微分方程降阶为2个一阶线性非齐次微分方程来进行求解,不需要考虑非齐次项的具体函数形式。该方法是求解二阶常系数非齐次微分方程的另一种有效途径,且更具一般性。This paper discusses the application of variable substitution method in solving second-order non-homogeneous differential equations with constant coefficients. For the second-order non-homogeneous differential equations with constant coefficients,variable substitution method can turn it into two one-order linear non-homogeneous differential equations and solve it without considering the exact form of the nonhomogeneous term.This method is another effective way to solve the second-order non-homogeneous differential equation with constant coefficients,and it is more general.

关 键 词：二阶常系数非齐次微分方程 变量替换 应用 

分 类 号：G642.0[文化科学—高等教育学]