Consider the following partial differential equation (PDE)
$$(y-1) \frac{\partial^{2} u}{\partial x^{2}}-(x-3)^{2} \frac{\partial^{2} u}{\partial y^{2}}+y^{2} \frac{\partial u}{\partial x}+x^{2} \frac{\partial u}{\partial y}+(x-y) u=0 .$$
Then, which of the following statements is/are true?
- In the region $\left\{(x, y) \in \mathbb{R}^{2}: y>1, x>3\right\}$, the PDE is hyperbolic
- In the region $\left\{(x, y) \in \mathbb{R}^{2}: y>1, x<3\right\}$, the PDE is elliptic
- In the region $\left\{(x, y) \in \mathbb{R}^{2}: y<1, x>3\right\}$, the PDE is elliptic
- In the region $\left\{(x, y) \in \mathbb{R}^{2}: y<1, x<3\right\}$, the PDE is hyperbolic
