 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/6/i/solution

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

Put

s = z - 1

and seek the leading Frobenius series term

y \sim s^{ρ}

y^{''}

and

y^{'}

become

- 2 s (1 + s)

and

2 + s

, respectively. The lowest power,

s^{ρ - 1}

, therefore has coefficient

- 2 ρ (ρ - 1) + 2 ρ

ρ (ρ - 2) = 0, ρ = 0, 2.

The term

- y

contributes only at the next order and does not enter this equation.

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