Abstract
We present a characterization of the second-order ordinary differential equations (ODEs) that can be linearized by means of certain nonlocal transformations. This characterization is given in terms of the coefficients of the equation and also determines the second-order ODEs that admit λ-symmetries and first integrals of some specific forms. Systematic methods to find these first integrals, λ-symmetries and the linearizing transformations are also derived.
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