A note on deriving linearizing transformations for a class of second order nonlinear ordinary differential equations

Abstract

We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as its first integral. We extract conditions for this integral to yield three different linearizing transformations, namely point, Sundman and generalized linearizing transformations. The explicit forms of these linearizing transformations are given. The exact forms and the general solution of the nonlinear ODE for these three linearizables cases are also enumerated. We illustrate the procedure with three different examples.