$($a$)$ Convert the equation del$\frac{}{d}$elt$-de{l}^2\frac{}{d}el{x}^2=0$ to an equivalent system by

introducing an auxiliary variable $p=$del$\frac{}{d}$elx. Show that the system is parabolic.

$($b$)$ Analyse del$\frac{}{d}$elt$-(de{l}^2\frac{}{d}el{x}^2+de{l}^2\frac{}{d}el{y}^2)=0$ in a similar way and show that it

is parabolic.