Abstract
An ordinary differential equation is an equation that involves a single unknown function, of a single variable, and some finite number of its derivatives. The order of a differential equation is the order of the highest order derivative of the unknown function that appears in the equation. The adjective ordinary is used to distinguish a differential equation from one that involves an unknown function of several variables, along with the partial derivatives of the function. A real solution of a differential equation is a function that, on some interval, possesses the requisite number of derivatives and satisfies the equation. A set of n linearly independent solutions of an nth-order linear homogeneous differential equation is called a fundamental set of solutions for the equation. The set of all functions that are solutions of a differential equation is called the general solution of the equation. The nonhomogeneous term is a function that is the solution of some linear homogeneous differential equation with constant coefficients.
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