Classification of Nonlinear Second-Order Differential Equations Admitting Certain Integrating Factors

Student: Ovsiannikov Maksim

Supervisor: Dmitry Sinelshchikov

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2021

Many processes in physics, mechanics and biology are described by the Lienard-type equations.Therefore, the search for new integrable cases of the Lienard equations is an important task.The classification of the Lienard-type equations admitting the quadratic integrating factors have never been obtained before. The first integral, containing information about the dynamics of differential equation, can be found using an integrating factor. In the present work the criteria for finding quadratic integrating factors from the Lienard-type equations are obtained. The results are illustrated by a number of examples of Lienard-type equations with quadratic integral factors, including physically significant equations.

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