We present a new method of finding general solution of linear and nonlinear ordinary differential equations of finite order by extending the Prelle-Singer method. We illustrate the underlying ideas of this method for second and third order ordinary differential equations in-detail with several non-trivial examples. Further, we discuss a new powerful method of identifying linearising transformations for the nonlinear ordinary differential equations of finite order. We derive the linearizing transformations from the first integral. Using the transformations we transform the nonlinear ordinary differential equations into free particle equation and obtain the general solution for the former. We also illustrate the theory with several nontrivial examples.
Contact A.P. Fordy (email: allan@maths.leeds.ac.uk ) for further details.
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