Q: Classify following PDEs as linear, semi -linear, quasilinear or fully nonlinear.Give order of PDEs.
a) $z_{xxt}+z^2z_{xt}+z_{tt}=\cot2x$
b) $z^2 z_{x}-(x^3z^3+y)z_{y}=-u^2x-4y$
c) $x^2 z_{x}-(x^3+5y)z_{y}+10z=\tan(zy)$
d) $z^2_{x}-(x^y+y)z_{y}+z=0$
My answers:
a) Third order semi linear PDE.
Firstly, I thought it is a quasi linear PDE. But then I think it is a semi linear PDE. Because the equation is third order PDE. And the term including lower derivatives than order of the equation can include dependent coefficient with respect to definition of semi linear.
b) First order quasi linear PDE
c) first order semi linear PDE
d) first order fully nonlinear PDE
Are they right?
