differential equation


An equation relating a variable that changes over time (referred to as a function), to its rate of change (referred to as its derivative). Many fundamental relationships in the natural world are described by differential equations, for example Newton's Second Law relates the force on a particle to the rate of change of that particle's linear momentum: F = d (mv) / dt. In this equation, the force on a particle (F) is equal to the rate of change over time (expressed by the derivative designation d / dt) of the particle's momentum (which is a product of the particle's mass [m] and velocity [v]).

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