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Foundation Mathematics for the Physical Sciences by K. F. Riley, M. P. Hobson

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14

Ordinary differential equations

Differential equations are the group of equations that contain derivatives. There are several different types of differential equations, but here we will be considering only the simplest types. As its name suggests, an ordinary differential equation (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 x2, exp x, ln x, sin x, etc. ...

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