# Integrating Factor and First Integrals of a Class of Third Order Differential Equations

## TL;DR

This paper extends the method of finding integrating factors to a specific class of third order differential equations, enabling their transformation into exact equations and reduction to second order.

## Contribution

It provides explicit forms of integrating factors for a class of third order differential equations, expanding the applicability of integration techniques.

## Key findings

- Explicit integrating factors are derived for certain third order equations.
- Conditions under which non-exact equations can be made exact are identified.
- Third order equations can be reduced to second order using these integrating factors.

## Abstract

The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor exists which transforms it to an exact one. Hence, it can be reduced into a second order differential equation. In this paper, we give explicit forms for certain integrating factors of a class of the third order differential equations.