Solving the Created Equations from Power Function Distribution

Abstract

      In this paper, a new class of ordinary differential equations is designed for some functions such as probability density function, cumulative distribution function, survival function and hazard function of power function distribution, these functions are used of the class under the study. The benefit of our work is that the equations ,which are generated from some probability distributions, are used to model and find  the  solutions  of problems in our lives, and that the solutions of these equations are a solution to these problems, as the solutions of the equations under the study are the closest and the most reliable to reality. The existence and uniqueness of solutions the obtained equations in the current study are discussed. The exact solutions of these obtained differential equations are calculated using some methods. In addition, the approximate solutions are determined by the Variation Iteration Method (VIM) and Runge-Kutta of 4^th Order (RK4) method. The chosen approximate methods VIM and RK4 are used in our study because they are reliable, famous, and more suitable for solving such generated equations. Finally, some examples are given  to illustrate the behavior of the exact and the approximate solutions of the differential equations with the scale parameters of power function distribution.