  A method of finding general solutions of second-order nonlinear ordinary
differential equations by extending the Prelle-Singer (PS) method is briefly
discussed. We explore integrating factors, integrals of motion and the general
solution associated with several dynamical systems discussed in the current
literature by employing our modifications and extensions of the PS method. In
addition to the above we introduce a novel way of deriving linearizing
transformations from the first integrals to linearize the second order
nonlinear ordinary differential equations to free particle equation. We
illustrate the theory with several potentially important examples and show that
our procedure is widely applicable.
