Differential equations

Differential equations are mathematical equations that relate a function with its derivatives, expressing how a quantity changes in relation to another. They play a crucial role in modeling dynamic systems across various fields, such as physics, engineering, biology, and economics. These equations can be ordinary or partial, depending on whether they involve single or multiple variables. Solving differential equations often requires techniques like separation of variables, integration factors, or numerical methods. The solutions provide insights into the behavior of systems over time, such as population growth, heat transfer, and mechanical motion, making them essential tools in understanding complex phenomena.