Particular Solutions of a Class of Nonhomogeneous Laplace Ordinary Differential Equations Encountered in Perturbation Analyses

摘要

Linear ordinary differential equations with polynomial coefficients are encountered in many disciplines of science and engineering. In the case of second order equations, the solution can very often be expressed in terms of elementary and/or special functions (Bessel functions, Legendre, Laguerre, Hermite, Tchebycheff polynomials, Hypergeometric functions, ...). Much fewer closed form solutions exist, however, for higher order equations. The Orr-Somerfeld equation of hydrodynamic stability and the equation of free vibration of clamped circular flexible spinning disks are two typical fourth order examples of this situation; their solutions do not appear to be representable in terms of elementary and/or special functions.