QUESTION $3$

Given the following PDEs:

$\frac{de{l}^2}{del{x}^2}+7(\frac{de{l}^2}{del{y}^2}{)}^3+=9$

$k\frac{de{l}^{2}T}{del{x}^2}-\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}=0$

${?}_{}+{(}_{xy}{)}^2+{?}^{}+12=0$

$\frac{de{l}^{2}u}{del{x}^2}+\frac{de{l}^{2}u}{del{y}^2}+4\frac{de{l}^{2}u}{\text{d}\text{e}\text{l}\text{y}\text{d}\text{e}\text{l}\text{z}}+4\frac{de{l}^{2}u}{del{z}^2}=0$

$($Equation$1)$

$($Equation $2)$

$($Equation $3)$

$($Equation $4)$

$3\mathrm{.}1$ Describe the order, degree, linearity, and homogeneity of the given equations.

$3\mathrm{.}2$ Classify Equations $2$ and $4$ into parabolic, elliptic, or hyperbolic $($show details of your

calculations$).$