A function for integration factors in solving equations

In this work we present a simple algorithm for computing integrating factors of certain classes of first order Ordinary Differential Equations (ODE), as well as the foundation of the algebraic basis for these methods. Matlab has been used to generate the algorithm for computing the integration factors. The aim of this paper is of a rather practical nature, i.e. the presentation of practical and efficient algorithm for the generation of integration factors for non – exact Ordinary Differential Equations, which can directly be implemented in the framework of a general purpose computer algebra system.

In this work we present a simple algorithm for computing integrating factors of certain classes of first order Ordinary Differential Equations (ODE), as well as the foundation of the algebraic basis for these methods. Matlab has been used to generate the algorithm for computing the integration factors. The aim of this paper is of a rather practical nature, i.e. the presentation of practical and efficient algorithm for the generation of integration factors for non – exact Ordinary Differential Equations, which can directly be implemented in the framework of a general purpose computer algebra system.

1997

A systematic algorithm for building integrating factors of the form µ(x, y ′ ) or µ(y, y ′ ) for nonlinear second order ODEs is presented. When such an integrating factor exists, the scheme returns the integrating factor itself, without solving any differential equations. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in solving non-linear examples from Kamke’s book is shown. (Submitted for publication in Journal of Symbolic Computation)

International Journal of Advanced Science and Engineering, 2023

The concept of function is one of the fundamental mathematical concepts, very important within mathematics itself as well as in the application of mathematics. Functions are an essential element of mathematical structuring and modeling of problems (e.g.in algebraic structures), as well as a means of comparing structures thus obtained (eg homomorphisms of structures). A mathematical function is a rule that gives the value of the dependent variable corresponding to certain values of one or more independent variables. A function can be represented in several ways, such as a table, formula, or graph. Apart from isolated points, the mathematical functions found in physical chemistry are single-valued. Apart from isolated points, the mathematical functions that occur in physical chemistry are continuous.

Eng. Appl. Sci. Lett., 2021

This paper discusses a gallery of useful results in connection with integrating factors that are often left as problems for discovery learning and are generally not taught in typical Ordinary Differential Equations courses. Most often than not the approach earlier writers employ is to give a possible form for an integrating factor that may results in an integrating curve without practical prove as far as the subject matter is concerned. In this write-up, an attempt is made by solving the resulting partial differential equation emanating from an underlining general differential equation of a non-exact form, by the use of the ratio theorem to establish various intricate possibilities of integrating factors that are seldom and often relegated to the background, even though they may be equally be applied as a function of a unitary variable or a linear combination of both the dependent and independent variables under certain conditions. Granted an integrating factor is found and such a function applied, the benefit is enormous especially the non-exact differential equation reduces into a known type which may be identified as exact, homogeneous, and or separable that yields a solution.

Introduces Partial derivatives and Exact Differential Equations, and describes the methods of solving them.

Плунгян В. А. I. Коммуникативная информация и порядок слов II. Пресуппозиции в словообразовании прилагательных / В.А. Плунгян ; Отв. ред. В.Ю. Розенцвейг. – М., 1983. – 52 с. – (Предварительные публикации / Ин-тут рус. яз. АН СССР ; Проблемная группа по эксперимент. и прикл. лингвистике. Вып. 149).

Плунгян В. А. I. Коммуникативная информация и порядок слов II. Пресуппозиции в словообразовании прилагательных / В.А. Плунгян ; Отв. ред. В.Ю. Розенцвейг. – М., 1983. – 52 с. – (Предварительные публикации / Ин-тут рус. яз. АН СССР ; Проблемная группа по эксперимент. и прикл. лингвистике. Вып. 149).