二阶常系数线性微分方程的降阶法  

Depression of Order for Two Order Linear Differential Equation with Constant Coefficients

作　　者：卢亦平[1] 钱椿林[1] 

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《苏州市职业大学学报》2014年第3期49-52,共4页Journal of Suzhou Vocational University

基　　金：苏州市职业大学青年基金资助项目(2010SZDQ12)

摘　　要：考虑二阶常系数线性微分方程的降阶法.首先,写出二阶齐次常系数线性微分方程的特征方程,求出特征方程的两个特征根;然后,利用积分因子乘以微分方程和导数的运算,将二阶常系数线性微分方程化为一阶微分形式;最后,将一阶微分形式两边同时积分,求解一阶线性微分方程,可求得二阶常系数线性微分方程的一个特解或通解.利用降阶法,可以求得微分方程的一个特解或通解.其计算方法简单和方便,在实际中具有应用价值.Depression of order for two order linear differential equation with constant coefficients is considered.First of all,the characteristic equation of linear differential equation with constant coefficients is written,and two characteristic roots are obtained,and then the differential equation is multiplied by the integral factor and operatied with derivative,the two order linear differential equation with constant coefficients is changed into the first-order differential form,and finally the first-order differential form is integrated.The two order linear differential equation becomes the linear differential equation of first order,solving first-order linear differential equations,and special or general solution of the differential equations can be obtained.The method is simple,convenient and very useful in practice.

关 键 词：二阶常系数线性微分方程 降阶法 特征根 一阶微分形式 

分 类 号：O175.1[理学—数学]