Ordinary differential equations (ODEs) are important in the field of mathematics due to their spread in various applications. Ordinary differential equations are of two types, one of which is equations with variable coefficients and the other is equations with constant coefficients, and there are many integral transforms have appeared that solve these equations. In this paper our aim is to present a new integral transform will call by Novel Mathematical transform and show how to apply it to solve ordinary differential equations with variable coefficient, also we can benefit from it in other research to solve equations with constant coefficients. Novel Mathematical transform is defined by the following integral: The purpose of this transform and any other transforms is to convert functions and equations from their original form to another simpler form, or at least another form known to us where in it, we transform the independent variable of the original function into another variable, thus changing the scope and extent of the original function. In This transform which is called Novel Mathematical transform or what is called Haneen Al-Zughair transform we used the exponent of the kernel as a rational function and the limits of integration as an exponential function, which we will use it. Also, we will find this transform for the fundamental functions and derivative, as well as some theorems, properties and inverse of this transform.

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Novel Mathematical Integral Transform for Solving Some LODEs

  • Haneen Jasim Azooz,
  • Ali Hassan Mohammed

摘要

Ordinary differential equations (ODEs) are important in the field of mathematics due to their spread in various applications. Ordinary differential equations are of two types, one of which is equations with variable coefficients and the other is equations with constant coefficients, and there are many integral transforms have appeared that solve these equations. In this paper our aim is to present a new integral transform will call by Novel Mathematical transform and show how to apply it to solve ordinary differential equations with variable coefficient, also we can benefit from it in other research to solve equations with constant coefficients. Novel Mathematical transform is defined by the following integral: The purpose of this transform and any other transforms is to convert functions and equations from their original form to another simpler form, or at least another form known to us where in it, we transform the independent variable of the original function into another variable, thus changing the scope and extent of the original function. In This transform which is called Novel Mathematical transform or what is called Haneen Al-Zughair transform we used the exponent of the kernel as a rational function and the limits of integration as an exponential function, which we will use it. Also, we will find this transform for the fundamental functions and derivative, as well as some theorems, properties and inverse of this transform.