Applied Mathematics & Information Sciences

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We study the linearization of nonlinear second-order ordinary differential equations from the point transformation viewpoint. A new algorithm for finding linearizing point transformation is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is in the general form. The general solution of this class of equations is obtained by solving the linearized equation and applying the point transformation. Moreover, we apply the obtained linearization criteria to the interesting problems of nonlinear ordinary differential equations, nonlinear partial differential equations and system of nonlinear ordinary differential equations.

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