 Solution

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

The product rule makes the drift term cancel:

u^{'} + β V^{'} u = e^{- β V} y^{'} .

Consequently the transformed eigenvalue problem is

- (D e^{- β V} y^{'})^{'} = λ e^{- β V} y, p = D e^{- β V}, q = 0, w = e^{- β V} .

Both

p

and the weight

w

are positive, as required for this Sturm-Liouville problem.

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