 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/12a/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

L {t^{n}} (s) = \frac{n}{s} L {t^{n - 1}} (s), L {1} = \frac{1}{s},

L {t^{n}} = \frac{n !}{s ^{n + 1}} .

e^{a t}

shifts the transform:

L {e^{a t} t^{n}} (s) = \frac{n !}{( s - a ) ^{n + 1}} .

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