Article

    Ufa Mathematical Journal
    Volume 4, Number 2, pp. 13-27

    Separation of an equation in the system of two second-order ordinary differential equations


    Bagderina Yu.Yu.

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    We consider projectable type systems of two second-order ordinary differential equations with cubic nonlinearity of right-hand side in first derivatives. For such systems we obtain criteria of reducibility by local transformation to a system with separating equation in one of unknown functions. Applications of the criteria and construction of the corresponding transformation is illustrated with a number of examples.