I want to turn this 2nd order equation into a system of first order equations but I am unsure about whether I can get rid of the $u$ or not
To write this as a system of equations so I can determine whether its semi-linear, quasilinear or nonlinear I thought that
$\eta \equiv u_y$
Form a system of 2 equations.
But $u$ is still in it? Does this say something about whether it is quasi-linear or not? Is $u\equiv u(x,y)$ still? If it is then the equation is in the form
I cannot tell what classification these equations have.