 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/7/c/solution

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

The cross derivatives are both

2 y

, so the equation is exact. The function

x cos x + x y^{2}

differentiates to the given one-form. Hence

x cos x + x y^{2} = C .

Differentiating this implicit equation checks both coefficients of the exact differential directly.

 New to topics? Read the docs here!