变系数线性微分方程算子解法的推广

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.

Generalization of Operator Method to Solve Linear Ordinary Differential Equations with Variable Coefficients

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 co...