 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iii/2/a/solution

u_{s} = 2 s u_{x} + 2 t u_{y}

and

u_{t} = - 2 t u_{x} + 2 s u_{y}

. Therefore

s u_{s} - t u_{t} = 2 (s^{2} + t^{2}) u_{x},

m = 2

. The

u_{y}

terms cancel identically, independently of the particular function

u

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