Complexity Analysis of the Rule based Cauchy’s Inequality in solving the n-order Differential Equations

This paper instigates the multivariate generalization of widely used Cauchy inequality 1 + x ≤ ex where can be any non-negative real number. The results this study solution for Cauchy’s problem particular Ordinary Differential Equation (ODE). is also related to complete monotone function and divided differences theory. proof based on empty product convention notion Beppo Levi theorem Monotone convergence. extended simultaneous inequalities. Key Words: ODEs, Inequalities, Population Dynamics, Simultaneous Divided differences.