View source for Quasi-linear equation

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A partial differential equation (cf. [[Differential equation, partial|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 $u$.

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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H.M. Luberstein,   "Theory of partial differential equations" , Acad. Press  (1972)  pp. 10; 12; 27</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  G.F. Carrier,   C.E. Pearson,   "Partial differential equations" , Acad. Press  (1976)  pp. Sect. 6.3; 89; 252</TD></TR></table>