 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/12/a/i/solution

The two coefficients are the corresponding partial derivatives of

e^{x + y}

. Therefore the differential form is exact, with

f (x, y) = e^{x + y} + C, df = e^{x + y} d x + e^{x + y} d y .

The arbitrary constant does not change the total differential.

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