Definition: Non-linear equations

A non-linear equation is an equation that doesn’t form a straight line when graphed. Nonlinear systems involve terms beyond linear or constant, like quadratic, cubic, exponential, and logarithmic functions. They’re described by equations where variables appear in polynomials of degree higher than one or in non-polynomial function arguments. The general representation of nonlinear equations is:

\$ax^2 + by^2 = c\$

Explanation:

The image displays a non-linear equation using x and y as variables, and a, b, and c as constants.

Definition: Non-linear equations in one variable

Non-linear equations in one variable are mathematical expressions where the variable is raised to a power other than 1 or appears in the denominator. This characteristic results in a curve that is not a straight line when plotted on a Cartesian plane. These equations can take various forms, including quadratic, cubic, trigonometric, or combinations of these types.

The general form of a non-linear equation in one variable can be expressed as follows: \$ ax^n + bx^(n-1) + cx^(n-2) + ..... + dx^2 + ex + f = 0\$.

Explanation:

Here the given image shows the non-linear equation in one variable where a, b, c, .., f are constants, x is the variable, and n represents the highest power of x in the equation.