2017/11/22 by Mohammadkheer Al-Jararha, Al-Jararha, Mohammadkheer
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Numerical methods for differential equations #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1711.08146
If the n-th order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Hence, its order can be reduced to the lower order. In this paper, the principle of finding an integrating factor of a none exact differential equations is extended to the class of n-th order differential equations Fn(t,y,y^′,y′′,…,y(n-1))y(n)amp;+Fn-1(t,y,y^′,y′′,…,y(n-1))y(n-1)+⋯ +
amp;+F1(t,y,y^′,y′′,…,y(n-1))y′+F0(t,y,y^′,y′′…,y(n-1))
amp;=0,where F0,F1,F2, ⋯,Fn are continuous functions with their first partial derivatives on some simply connected domain Ω⊂\Rn+1. In particular, we prove some explicit forms of integrating factors for this class of differential equations. Moreover, as a special case of this class, we consider the class of third order differential equations in more details. We also present some illustrative examples.