SOME CLASSES OF RICCATI EQUATIONS INTEGRABLE IN QUADRATURES

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Journal of Universal Mathematics
Volume:6 Issue:1
SOME CLASSES OF RICCATI EQUATIONS INTEGRABLE IN QUADRATURES

SOME CLASSES OF RICCATI EQUATIONS INTEGRABLE IN QUADRATURES

Authors : Anarkul URDALETOVA, Olga ZABİNYAKOVA, Syrgak KYDYRALİEV

Pages : 81-88

Doi:10.33773/jum.1140210

View : 35 | Download : 16

Publication Date : 2023-01-31

Article Type : Research Paper

Abstract :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 insert ignore into journalissuearticles values(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.
Keywords : Ordinary linear differential equations, differential equation with variable coefficients, Euler equations, Riccati equations, integrated by quadratures, the chain method for differential equations solving

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