SOME CLASSES OF RICCATI EQUATIONS INTEGRABLE IN QUADRATURES

Yıl 2023, Cilt: 6 Sayı: 1, 81 - 88, 31.01.2023

Anarkul Urdaletova , Olga Zabinyakova , Syrgak Kydyraliev

https://doi.org/10.33773/jum.1140210

Öz

As it is known, the second-order ordinary linear differential equation with variable coefficients is solvable in case if related Riccati equation can be integrated by quadratures. This paper considers establishment of correspondence between such equations by the authors’ method which means the second-order equation representation by a chain of the first-order equations. The algorithm of special Riccati equation solving is demonstrated (coefficients of these Riccati equations satisfy special conditions). One more peculiarity of this paper stands in consideration of exact applicational example – the Riccati equation which describes the magnetotellurics impedance behavior in geological media.

Anahtar Kelimeler

Ordinary linear differential equations, differential equation with variable coefficients, Euler equations, Riccati equations, integrated by quadratures, the chain method for differential equations solving

Destekleyen Kurum

American University of Central Asia AND Kyrgyz-Turkish Manas University AND Research Station of RAS in Bishkek city

Kaynakça

• Reference1 S.K. Kydyraliev, A.B. Urdaletova Solving Linear Differential Equations by Operator Factorization. The College Mathematics Journal, USA, 27(3), pp. 199-204, (1996).
• Reference2 S.K. Kydyraliev, A.B. Urdaletova, E.S. Burova Advantages of the chain method for solving linear differential and difference equations. Bulletin of the Kyrgyz-Russian Slavic University, 20(8), pp. 16-20, (2020).
• Reference3 S.K. Kydyraliev, A.B. Urdaletova The linear ordinary differential equations’ solution formula. Bulletin of the Kyrgyz-Russian Slavic University, 20(8), pp. 11-15, (2020).
• Reference4 A. D. Polyanin, V. F. Zaitsev Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems. Chapman & Hall/CRC Press, Boca Raton, 1496 p., (2017)
• Reference5 M.N. Berdichevskii, V.I. Dmitriev Magnetotelluric Sounding of Horizontally Homogeneous Media. Мoscow, Nedra, 250 p. (1992)