The Exact Linearization of Some Classes of Ordinary Differential Equations for Order n > 2

The method of exact linearization nonlinear ordinary differential equations (ODE) of order n suggested by one of the authors is demonstrated in [1, 2]. This method is based on the factorization of nonlinear ODE through the first order nonlinear differential the operators, and is also based on using both point and nonpoint, local and nonlocal transformations. Exact linearization of autonomous the third, the fourth and the fifth orders ODE is presented in this paper. For the first time general form of autonomous fourth [3] and fifth order equations, admitting exact linearization with using nonpoint transformation is found by second of the authors. We obtain the formulas in quadratures for finding general and partial solutions of investigated classes of equations. For the realization of transformations and construction of the considered equations we used the computer algebra system MAPLE.