Department of Physics and Astronomy
Brigham Young University
Provo, Utah 84604 U.S.A.

e-mail: harrison@physics.byu.edu

An Old Problem Newly Treated With Differential Forms: When and How Can the Equation y'' = f(x,y,y') Be Linearized?

Abstract:
Sophus Lie, more than a century ago, investigated the problem of linearization of the equation y'' = f(x,y,y'), where ' means d/dx.  Originally, he investigated the necessary conditions for linearization and showed that f must be a cubic in y' and that other conditions must be satisfied.  Later, he and others such as Tresse worked out actual construction of the linearizing transformations, often using group theory.  The present author will show a method of construction using differential forms, suitable when certain intermediate equations can be integrated explicitly.