 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-3/33a/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

n

pr^{(n)} V = V + \sum_{j = 1}^{n} η^{(j)} \partial_{u^{(j)}}, η^{(j)} = D_{x} η^{(j - 1)} - u^{(j)} D_{x} ξ, η^{(0)} = η,

where

D_{x}

pr^{(1)} V = ξ \partial_{x} + η \partial_{u} + [η_{x} + (η_{u} - ξ_{x}) u^{'} - ξ_{u} (u^{'})^{2}] \partial_{u^{'}} .

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