Generalized Weierstrass Integrability of a Class of Second-order Nonlinear Differential Equations

The generalized Weierstrass integrability of a class of second-order nonlinear differential equations is considered. The conditions of existence and the corresponding expressions of generalized Weierstrass inverse integrating factors of the second-order nonlinear differential equation are presented. The relationship between the generalized Weierstrass inverse integrating factors and the Weierstrass inverse integrating factors is given. Finally, as an application of the main results, a Kudryashov-Sinelshchikov equation for obtaining traveling wave solutions is considered.

General Solution Of Nth-Order Linear Ordinary Differential Equation

In this paper we present a solution expression for the general Nth-order linear ordinary differential equation as our main result which involves the use of Integrating Factors where the Integrating Factors are determined using a set of equations such that when this set of equations can be solved, the solution of the concerned differential equation can be determined completely. In this regard we also present result for a special case corresponding to the main result where the solution of the general Nth-order linear ordinary differential equation can be determined completely when N-1 out of N complementary solutions are known.

Frame Agreement For Cross-Border Cooperation Between Local Authorities

The cross-border cooperation of local authorities, taken up based on the administrative law of each of the states, is marked by both integrating factors that refer to the similarities of the applicable system of law and separating factors arising from the principle of territoriality of administrative law. The frame agreement is a smart solution (a smart tool) of cross-border cooperation, because it enables cooperating territorial self-government units to conduct a unique operation of ‘recompensing’ separating factors with integrating factors.

λ-Symmetry and μ-Symmetry Reductions and Invariant Solutions of Four Nonlinear Differential Equations

On one hand, we construct λ-symmetries and their corresponding integrating factors and invariant solutions for two kinds of ordinary differential equations. On the other hand, we present μ-symmetries for a (2+1)-dimensional diffusion equation and derive group-reductions of a first-order partial differential equation. A few specific group invariant solutions of those two partial differential equations are constructed.

An Applied Mathematical Model for Business Transformation

The original HMM uses a natural language- or behaviour-driven development environment that can be adopted by development teams by using and integrating factors' categories in their system; that is why the authors propose the use of the holistic critical success factors management system (HCSFMS), and they implement a proof of concept (PoC) to prove this chapter's concept feasibility and levels of integration risks. The HCSFMS supports decision-making systems (DMS), business transformation projects, and enterprise architecture projects (EAP) (or simply the project). The PoC is based on a fictious case from the insurance domain.

A Note on Integrating Factors of a Conformable Fractional Differential Equation

Recently exact fractional differential equations have been introduced, using the conformable fractional derivative. In this paper, we propose and prove some new results on the integrating factor. We introduce a conformable version of several classical special cases for which the integrating factor can be determined. Specifically, the cases we will consider are where there is an integrating factor that is a function of only x, or a function of only y, or a simple formula of x and y. In addition, using the Conformable Euler's Theorem on homogeneous functions, an integration factor for the conformable homogeneous differential equations is established. Finally, the above results apply in some interesting examples.