Resonance method commonly used for Painlevé classification of ordinary differential equations often detects negative resonances, other than a trivial one of –1 (which should always be present). However, it is asserted by some researchers that the nature of these negative resonances is not fully understood. The problem arises as how to use negative nontrivial resonances to obtain information about the analytical properties of solutions of non-linear differential equations, in particular, to construct rational solutions. In the present paper, the method for constructing rational solutions f certain classes of autonomous non-linear ordinary differential equations is presented.
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