Any function in which the dependent variable is not exactly proportional to the zeroth or first power of the independent variable. E.g.: y(x) = a*(x+x^3); y(x) = a*exp(x); y(x) = a*sin(x); etc.
This may be extended to differential equations by stating a nonlinear differential equation is one in which some function depends on a derivative which is not to the zeroth or first power. An example is: dy/dx - (y(x))^2 = a.
Note, all of the values for "a" in these examples are meant to be constants.
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linear, if side is x then perimeter is 4x
If you mean y = x2, then yes, it is nonlinear.
y=x2 and y=lnx are two examples of nonlinear equations.
Nonlinear scaling is a scaling where the difference between each major unit of measure is not the same. For example, see logarithmic scale.