ordinary differential equations

The document provides an overview of ordinary differential equations (ODEs), fundamental in modeling dynamic systems. It explains the basic types, including first-order, second-order, linear, and nonlinear ODEs. Key methods for solving ODEs, such as separation of variables, integrating factors, and numerical techniques, are detailed. The notes emphasize the importance of initial conditions and solutions' uniqueness. Real-world applications in physics, engineering, and biology illustrate the pra...