Exactness of Second Order Ordinary Differential Equations and Integrating Factors

Abstract

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

Key words and phrases. Second order differential equation, Exact equations, nonlinear differential equations, Non-exact equations, Integrating factor.

2000 Mathematics Subject Classification. 34A25, 34A30