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A variable coefficient is a term used in mathematics, particularly in the study of differential equations, to describe a coefficient that is not a constant but rather a function of one or more independent variables. In a linear differential equation, for example, the coefficients of the dependent variable and its derivatives are typically constants. However, when these coefficients change depending on the independent variable, the equation is said to have variable coefficients.
Equations with constant coefficients can often be solved using standard analytical techniques, such as characteristic equations.
The study of variable coefficient differential equations is crucial in many areas of science and engineering.