1. Classify the following partial differential equations as elliptic, parabolic or hyperbolic.If the classification depends on the values of the independent variables r and y, give the classification for each

different region in the x-y plane. \text { a. } \frac{\partial^{2} u}{\partial x^{2}}+2 \frac{\partial^{2} u}{\partial x \Delta y}+\frac{\partial^{2} u}{\partial y^{2}}+\frac{\partial u}{\partial x}=0 \text { b. } x \frac{\alpha^{2} \mathrm{u}}{\partial x^{2}}+y \frac{\partial^{2} u}{\partial y^{2}}+x^{2} \frac{\partial u}{\partial y}=0 \text { c. } 2 \cos x \frac{\partial^{2} u}{\partial x^{2}}+2 \frac{\partial^{2} u}{\partial x_{y} y}+\cos x \frac{d^{2} n}{d y^{2}}+\sin x\left(\frac{\partial u}{\partial x}+\frac{\partial u}{b y}\right)=0