A nonlinear equation is any equation that cannot be written in the linear form Ax + By + C = 0. Common examples include curves such as y = x², y = x³, and y = cos(x), as well as equations that multiply variables together (for example xy = 12) or place a variable in a denominator (such as y = 1/x).
In algebra courses, systems that mix a line with a parabola or a circle are classic nonlinear systems: OpenStax defines a nonlinear equation as any equation that cannot be written in that linear form. Source: OpenStax College Algebra 2e — Systems of Nonlinear Equations.