 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/15/b/i/solution

v = u^{'} + 3 u

. Differentiate it and eliminate

v^{'}

u^{''} = - 3 u^{'} + v^{'} = - 3 u^{'} - 5 u + v = - 3 u^{'} - 5 u + u^{'} + 3 u .

u^{''} + 2 u^{'} + 2 u = 0 .

Conversely, a solution of this equation together with

v = u^{'} + 3 u

solves both original equations, so the elimination loses no solutions.

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