Firstly, I know that both $\frac{\partial^2 u}{\partial x^2}=0$ and $\frac{\partial^2 u}{ \partial y^2}=0$ are second order differntial equation but what is the order of $\frac{\partial^2 u}{\partial x \partial y}=0$?
Secondly, what is the degree of the differential equations $\left(\frac{\partial^2 u}{\partial x^2}\right)^7+\left(\frac{\partial^2 u}{\partial y^2}\right)^5+\left(\frac{\partial^2 u}{\partial x\partial y}\right)^3=0$ and $\left(\frac{\partial^2 u}{\partial x^2}\right)^7+\left(\frac{\partial^2 u}{\partial x^2}\right)^3=0$.
