 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/15/a/i/solution

m = - 2

, because both

e^{- 2 x}

and

x e^{- 2 x}

occur as independent solutions. Hence its characteristic polynomial is

(m + 2)^{2} = m^{2} + 4 m + 4.

Comparing constant terms gives

γ = 4 .

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