 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/13/a/i/solution

Differentiate the second ordinary differential equation and use the first to eliminate

x^{'}

y^{''} = x^{'} - sin t = β y + sin t - sin t .

y^{''} - β y = 0 .

No solutions are lost: given a solution

y

x = y^{'} - cos t

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