Question 1: (6 marks) (x2 + y2 – 1) 224 Verify that the following second order partial differential equation: 202u อาน +

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Question 1: (6 marks) (x2 + y2 – 1) 224 Verify that the following second order partial differential equation: 202u อาน + +(x2 + y2 – 1) ) = 0 is: дх2 дхду ду2 a. Parabolic in the region x2 + y2 > 2 b. Elliptic in the region 0 < x2 + y2 <2 c. Hyperbolic in the region () < x2 + y2 <2 Please give a conclusion for each case given above. Question 2: (6 marks) Use the appropriate method to classify the following second-order partial differential equations: +(x - 1) 372 อน 22u дх2 a. 0 b. Uzx + Uyy+ Uzz+ Uyz+ Uzy = 0 c. Uxx + 2uyy + Uzz = 2uxy + 2uyz