 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/16/a/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

d (1 - y) / (1 - y) = - 3 d x / x

. Thus

1 - y = C x^{- 3}

x > 0

, and the initial value gives

C = 1

. Hence

y = 1 - x^{- 3}, x > 0.

The initial-value branch cannot cross its singularity at zero.

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