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Ordinary differential equations (DE) represent a very powerful mathematical tool for solving numerous practical problems of science and engineering. This chapter treats of the most important types of first-order DEs, the techniques of their solution and their wide range of applications.The Chapter is organized as follows:1. Basic Concepts.2. First-order Differential Equations: General concepts, DEs with separated and separable variables, Homogeneous DEs, DEs that can be reduced to a homogeneous DE, Exact DEs, Integrating Factors, Linear DEs, DEs reducible to linear form: the Bernoulli, Riccati, Clairaut and Lagrange equations.3. Applications of the first-order DEs: Geometric Applications, Elementary Mechanics, Laws of Exponential Growth and Decay.