算子1/(D+P(x))在微分方程中的应用

Application of the Operator in Differential Equation

本文应用算子1/[D+P(x)],归纳出线性微分方程(D+P_1(x))(D+P_2(x))·…·(D+P_n(x))y=f(x)的通解典型表达式,从理论上给出其有解的充分必要条件。

This paper induces the modal expression of general solution of the linear differential equation using operator 1 / (D+P(x)), and gives the necessary and sufficient conditions of solubility in theory.