Logarithmic Integration Method for Solving of First and Second Order Differential Equations

TL;DR

This paper introduces logarithmic integration methods for efficiently solving first and second order ordinary differential equations by leveraging properties of derivatives and logarithms to simplify the equations.

Contribution

It presents a novel logarithmic approach for solving differential equations, extending potential applications to higher order equations.

Findings

Effective reduction of equation complexity

Applicable to first and second order equations

Potential for extension to higher order equations

Abstract

In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of terms in the equation. Here we carry out this only for equations of the first and second order. Similar methods can also be used to obtain solutions to higher order equations.