**6**

**Higher-order ordinary differential equations**

Differential equations are the group of equations that contain derivatives. Chapters 6–11 discuss a variety of differential equations, starting in this chapter with those ordinary differential equations (ODEs) that have closed-form solutions. As its name suggests, an ODE contains only ordinary derivatives (no partial derivatives) and describes the relationship between these derivatives of the *dependent variable*, usually called *y*, with respect to the *independent variable*, usually called *x*. The solution to such an ODE is therefore a function of *x* and is written *y*(*x*). For an ODE to have a closed-form solution, it must be possible to express *y*(*x*) in terms of the standard elementary functions such as ...

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