A equação não linear is an equation that does not form a straight line when graphed on a coordinate plane. This means that the relationship between the variables is not proportional, and the variables may be raised to powers greater than one, multiplied together, or involve other non-linear operations como funções exponenciais, logarítmicas ou trigonométricas.
Em contraste com as equações lineares, que podem ser expressas na forma y = mx + b (where m is the slope and b is the y-intercept), non-linear equations can take various forms. Examples include quadratic equations like y = ax² + bx + c, polynomial equations of higher degrees, and equations involving square roots or trigonometric functions.
Equações não lineares são importantes em muitos campos, incluindo physics, engineering, economics, and inteligência artificial, as they often describe sistemas complexos and relationships. For instance, in aprendizado de máquina, non-linear models can capture more intricate patterns in data than linear models can.
Resolver equações não lineares pode ser mais desafiador do que resolver equações lineares, as they may have multiple solutions or none at all. Techniques such as numerical methods, graphical methods, or iterative algorithms are often employed to find solutions to non-linear equations.