摘要
运用微分算子运算的基本原理,证明最高项系数含有函数的变系数线性微分算子可分解为一阶微分算子及其幂的因式的乘积的充要条件,并得到常见的最高项系数含有函数的二阶变系数线性微分算子可分解的充要条件;应用积分运算的基本方法,推导出由微分算子分解式求出已知方程通解的方法和步骤,并得到了具体的计算公式;通过实例分析和比较说明所得到解法的应用及其具有的优越性.
Using differential operators,the necessity and sufficient on the existence of first-order factors of linear differential equations with function as coeffcients of the highest term are proved.The necessary and sufficient conditions are shown for the second-order factors of linear differetial operators with variable coefficients.The integration methods are used to find general solutions to differential equations using differential operators.Examples are given to analyze and compare the proposed method with conventional methods.
出处
《汕头大学学报（自然科学版）》
2011年第1期18-26,共9页
Journal of Shantou University：Natural Science Edition
关键词
一般推广
变系数
线性微分算子
算子分解
算子解法
generalization
variable coefficient
linear differential operator
factorization of the operator
operator method
