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We begin a study of first-order ordinary differential equations.

In the following sections, we will study some basic ordinary differential equations, which are equations that involve an unknown function (rather than simply an unknown number) and its derivatives. In our case, we will restrict attention to first-order ODEs, which involve only the unknown function $y(x)$, its parameter $x$, and its derivative $y'(x)$. We will discuss how to numerically and graphically approximate solutions of such ODEs, study two important types of first-order ODEs, and see some applications of these ODEs to various geometric and physical problems.