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Let y(x) solve the differential equation (x*ln x)*dy/dx + y = 2x*ln x for x >= 1. Find y(e).

1. 2
2. 2e
3. e
4. 0

Correct answer: 2

Solution

Using integrating factor ln x, the solution gives y*ln x = x*ln x - x + C; applying boundary behaviour and evaluating at x = e yields y(e) = 2.

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