 Solution

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

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

Let

Δ (x, u, u^{'}) = u^{'} - F (x, u)

. Applying the first prolongation gives

pr^{(1)} V (Δ) = η_{x} + (η_{u} - ξ_{x}) u^{'} - ξ_{u} (u^{'})^{2} - ξ F_{x} - η F_{u} .

Δ = 0

, one has

u^{'} = F

. The infinitesimal symmetry criterion is therefore exactly

0 = η_{x} + (η_{u} - ξ_{x} - F ξ_{u}) F - ξ F_{x} - η F_{u} .

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