Differential Equation/Examples/Second Order Second Degree Non-Linear Partial

Example of Differential Equation

Partial non-linear differential equation of the $2$nd order and $2$nd degree in $2$ independent variables:

$\dfrac {\partial^2 z} {\partial x^2} \cdot \dfrac {\partial^2 z} {\partial y^2} - \paren {\dfrac {\partial^2 x} {\partial x \partial y} }^2 = 0$

Sources

• 1926: E.L. Ince: Ordinary Differential Equations ... (previous) ... (next): Chapter $\text I$: Introductory: $\S 1.1$ Definitions