# Quasi-linear equation

A partial differential equation (cf. Differential equation, partial) that is linear with respect to the leading derivatives of the unknown function. For example, the equation

$$\left(\frac{\partial u}{\partial x}\right)^2\frac{\partial^2u}{\partial x^2}+\frac{\partial u}{\partial y}\frac{\partial^2u}{\partial y^2}+u^2=0$$

is a second-order quasi-linear equation with respect to the unknown function $u$.