本文提出几种高阶变系数线性偏微分方程并给出了它们的分离变量解,这些方程及其解的重要特点在于它们是公式化的,方程是变系数的.正因为这样,我们可以把为数众多的、目前尚未求得其精确解的偏微分方程纳入本文方程,从而直接获得它们的精确解.本文定理在空气动力学、流体动力学、弹性体振动和平衡、热传导等许多问题和领域中均有广泛的应用,限于篇幅,文中仪列举了少量的应用例子.本文方程及其解在低阶时均易直接验证它们的正确性.由于本文方程的解是用不定积分表示的,因此还可用文献[1]中的方法算出其数值解.

In this paper some higher order linear partial differential equations with variable coeffidents and their solutions formulas are given. Since the coeffficients of these equations are general, many linear partial differential equations, which are difficult to solve, can be found in these equations by selecting the variable coefficients and can be solved by the formulas presented, we have solved many linear partial differential equations arising from aerodynamics, elastic vibrations, inhomogeneous wave equation and other fields by means of these formulas. Moreover, the numerical solutions can also be obtained from these formulas by means of a method presented by Feng Kang.