We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the nth-order differential equation to a system of n linear differential equations with unit...

The aim of this paper is to find the class of continuous pointwise transformations (as general as possible) in the framework of which Kummer’s transformation z(t) = g(t)y(h(t)) represents the most general pointwise transformation converting every linear homogeneous differential equation of the nth order into an equation of the same type. Further, some forms of these equations having certain sub...

Recent developments have shown that the widely used simplified differential model of Eringen’s nonlocal elasticity in nanobeam analysis is not equivalent to corresponding and initially proposed integral models, pure two-phase model, all cases loading boundary conditions. This has resolved a paradox with solutions are line expected softening effect theory appears other cases. In addition, it rev...