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Essential Mathematical Methods for the Physical Sciences by K. F. Riley, M. P. Hobson

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6

Higher-order ordinary differential equations

Differential equations are the group of equations that contain derivatives. Chapters 611 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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