Studying the (n-1)-th Order Riccati Type Characteristic Equations of Linear Differential Equations in the Form of Algebraic Equations
Kazbek A. Khasseinov *
Department of Mathematics, Kazakh National Technical University named after K.I. Satpayev Republic of Kazakhstan, 22 Satpayev St., P.O. 050013, Almaty, Kazakhstan
*Author to whom correspondence should be addressed.
Abstract
From existence of analogies between problems of integrating Linear differential equations (LDE) in quadratures and solution to algebraic equations in radicals and based on studying properties of the latter in the article we have found one special differential equation. By studying characteristic equation of Riccati type and linking it to an algebraic equation we have obtained a recurrent LDE with variable coefficients and have established its properties.
Keywords: Characteristic equations of riccati type, recurrent differential equation