Differential equations are mathematical equations that relate a function to its derivatives, expressing how a quantity changes over time or space. They are fundamental in modeling various phenomena in physics, engineering, biology, and economics, among other fields. The main characteristics include ordinary differential equations (ODEs), which involve functions of a single variable, and partial differential equations (PDEs), which involve multiple variables. Common use cases for differential equations include modeling population dynamics, heat transfer, and motion of objects. Solving these equations can provide insights into the behavior of complex systems.
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