SOLVING FINITE-ORDER LINEAR DIFFERENTIAL EQUATIONS USING THE CHAIN METHOD

Differential equations are a powerful tool for modeling and solving problems in many branches of science.Of particular importance in the study of differential equations are difference equations, which describe the behavior of discrete systems.Physical, economic, and social processes evolve over time and are dynamic processes characterized by their speed.Therefore, many of them are described by differential equations.Difference equations arise, for example, in discrete-time models of economic dynamics.Difference equations have been studied in detail in [1 -6].Consider a linear difference equation of order n: l n+k = a 1k l n+k-1 + a 2k l n+k-2 + ⋯ + a nk l k, a nk ≠ 0, k = 0, 1, …, (1) where a 1k , a 2k , …, a nk are known functions of integer argument k.A step-by-step solution of equation ( 1) is used, i.e. at each subsequent step of using equation (1), the solutions found in the previous steps are taken into account, and writing the coefficients of equation (1) in the form a jk does not allow establishing the