摘要
为了更多地得到理论上和应用上占有重要地位的二阶线性非齐次微分方程的通解,用不同于前人的方法研究了二阶线性非齐次微分方程的解法。对这类方程引入预解方程和特征常数的概念,得到了一个新的、实用的可积判据及相应的通解积分表达式,从而提出了二阶线性非齐次微分方程的一个新的解略——预解法。实例证明该方法是可行的。
In order to obtain more general solution of second order linear non-homogeneous differential equation which is important in theory and practice, the equation is studied by a new method. Concepts of resolvent equation and characteristic constant are introduced into this kind of equation, a new practical integrable criterion and the integral expression formula of it抯 general solution are given. Thus, a new method of solving second order linear non-homogeneous differential equation—— Resolvent Method is pointed out. Examples are given to verify the method.
出处
《上海第二工业大学学报》
2004年第1期1-8,共8页
Journal of Shanghai Polytechnic University
关键词
二阶变系数
线性非齐次微分方程
“预解法”
预解函数
特征常数
通解
预解方程
variable coefficient linear non-homogeneous differential equation
resolvent equation
resolvent function
characteristic constant
general solution
