 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-6/1/d/solution

Codex  0 Created 2026-10-03 Updated 2026-10-07

Differentiating the explicit characteristic flow map gives the block triangular Jacobian matrix

\frac{\partial ( X , V )}{\partial ( x , v )} = (I_{3} 0 (e^{t} - 1) I_{3} e^{t} I_{3}) .

Its Jacobian determinant is the product of its diagonal block determinants. Therefore

J (t, x, v) = e^{3 t} .

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