THE RELATIONSHIP BETWEEN CLASSICAL AND MODERN METHODS OF SOLVING FIRST AND SECOND-ORDER DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS

This article discusses the relationship between classical and modern methods for solving first and second-order differential equations, as well as the differences in their solutions. Classical methods are based on analytical solutions, whereas modern methods utilize numerical techniques to solve complex equations. The connection between these methods is explained, and their role in mathematical modeling is analyzed. Modern methods, with the help of computers, offer extensive opportunities for modeling large and complex systems.