 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/13/b/ii/solution

The real equation has domain

x > 0

μ (x) = exp (\int (1 + ln x) d x) = e^{x l n x} = x^{x} .

(x^{x} y)^{'} = x^{x} x^{- x} = 1

. After integration,

x^{x} y = x + C

2 = 1 + C

, hence

y (x) = (x + 1) x^{- x}, x > 0.

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