 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2/15/b/iii/solution

u = v^{'}

fixes

u

from the same two constants:

u (t) = 2 A e^{2 t} - 2 B e^{- 2 t} .

Indeed

u^{'} = 4 A e^{2 t} + 4 B e^{- 2 t} = 4 v + 2

, so both original equations hold. No further independent integration constant is available in this two-dimensional linear system of ordinary differential equations.

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