A constant whose value does not depend on, and is not constrained by, any other variable or constant in a mathematical equation. Further information may serve to fix its value. The most common example is in solutions to differential equations, where one equation will have many solutions, each distinguished by the values of one or more arbitrary constants. For example, the differential equation $dy/dx=3$ has solutions of the form $y=3x+C$, where C is an arbitrary constant. If we have further information about the initial conditions, e.g. that $y=9$ when $x=0$, then we can determine that in this case C must equal 6.