Traditionally the Euler method is used for solving systems of linear differential equations. The method is based on the use of eigenvalues of a system's coefficients matrix. Another method to solve those systems is the D'Alembert integrable combination method. In this paper, we present a new method for solving systems of linear differential and difference equations. The main idea of the method is using the coefficients matrix eigenvalues to find integrable combinations of system variables. This method is particularly advantageous when nonhomogeneous systems are considered.
In addressing the dynamic phenomena in our reality, algebraic methods might be insufficient, as they are primarily suited for static problems. Instead, equations involving varying quantities offer a more fitting framework. Differential equations, containing derivatives, embodying the rate of change, can be used as a tool for capturing evolving realities. This paper explores the direct integration technique for linear differential equations, drawing on principles from both the Euler and D'Alembert methods. Moreover, we illustrate the practical application of these differential equations, partic ...Дагы
Anarkül URDALETOVA
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