CONNECTION BETWEEN CLASSICAL AND MODERN METHODS FOR SOLVING FIRST AND SECOND-ORDER DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS

Аннотация

This article examines the relationship between classical and modern methods for solving first and second-order differential equations and the differences in their solutions. Classical methods are based on analytical solutions, while modern methods utilize numerical techniques to solve complex equations. The connection between classical and modern methods is explained, and their role in mathematical modeling is analyzed. Modern methods, with the aid of computers, provide significant opportunities for modeling large and complex systems. Keywords: Method of undetermined coefficients, solving homogeneous and nonhomogeneous equations, finite element method, analytical solution, boundary value methods.