Direct Integration of Systems of Linear Differential Equations and Some Economic Applications

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, particularly systems of linear differential equations, within economic modeling contexts. Through this exploration, we show how mathematical tools unveil the dynamics inherent in economic systems, providing insights crucial for analysis and prediction.