SOME CLASSES OF RICCATI EQUATIONS INTEGRABLE IN QUADRATURES

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.

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