Studying the (n-1)-th Order RiccatiType Characteristic Equations of LinearDifferential Equations in the Form of AlgebraicEquations

摘要

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.