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This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and    . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation   and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.

applied mathematics

Criteria for System of Three Second-Order Ordinary Differential Equations to Be Reduced to a Linear System via Restricted Class of Point Transformation