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Calculus Level 3

\[\large y' = \ln(xy' - y)\]

Given the differential equation above, \(y(1) = -1\), \(y\) is twice differentiable, and \(y''(x) \ne 0.\)

Evaluate \(y(e)\).

\(\)
Notation: \(e \approx 2.7182\) denotes the Euler's number.

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