CONSTANT , ARBITRARY CONSTANT AND VARIABLE
In mathematics, a constant is a value that does not change and remains the same throughout the problem or equation. For example, in the equation y = 2x + 5, 2 and 5 are constants because they do not depend on the value of x.
An arbitrary constant is a constant that appears in a solution to a differential equation or an indefinite integral, where its value is not determined by the given initial conditions or limits of integration. The arbitrary constant represents all possible solutions to the equation. For example, the indefinite integral of f(x)dx is F(x) + C, where C is an arbitrary constant.
A variable, on the other hand, is a symbol or quantity that can take on different values in a given problem or equation. It is usually represented by a letter, such as x, y, or z. In algebra, variables are often used to represent unknown values in equations or formulas.
In summary, a constant is a fixed value that does not change, an arbitrary constant is a constant that appears in a solution to an equation, and a variable is a quantity that can take on different values in a given problem or equation.
IN SIMPLE LANGUAGE ------
constant - fixed and known
arbitrary constant - fixed and unknown
variable - not fixed and unknown
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