【摘要】 <正> 线性常微分方程有着广泛的应用。常系数线性方程及其代数解法已是力学、电学及工程技术中的重要解析工具。在一般的系数激励振动、波导传输理论以及其它许多系统中,人们还常会遇到高阶变系数线性方程或可化为这种方程的一阶线性方程组。如果能求出它们的解析解,将对有关问题的归纳、分析与应用大有帮助。 在文献[4]中,我们利用Riccati方程的几类新的可积类型给出了二阶变系数线性方程的几类新的可积类型,积出了更多还原

【Abstract】 In §1, two methods for solving the second order homogeneous linear ordinary differential equation with variable coefficients are given, which are different from the one in [4].In §2,we give several classes of higher order linear differential equations with variable coefficients such as which can be solved by using the two methods.The same order Euler equations and equations with constant coefficients are all their special cases. Following [4], we present the concepts of the resolvent function, the characteristic constant and the characteristic equation.Thus, the equations mentioned above can be solved by means of algebra.In §3 we give two classes of nth-order ordinary differential equations with variable coefficients and which can be reduced to those with constant coefficients,and give two classes of sol vable systems of equations.In §4, the sufficient conditions or the necessary and sufficient conditions under which several classes of homogeneous linear differential equations with periodic coefficients possess nontrivial periodic solutions are given.更多还原