 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/3/b/solution

y_{p} (x) = \int_{a}^{b} G (x, z) f (z) d z .

The delta identity gives

L y_{p} = f

and the endpoint conditions follow from those of

G

. If a nonzero homogeneous solution also satisfies both endpoint conditions, it may be added; uniqueness is not automatic in that case.

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