You are given the differential equation \( \frac{dy}{dx} + y \ln x = x^{-x} e^{-x} \) and the initial condition \( y(1) = 0 \)

If the value of \( y(2) \) can be written in the form \( \dfrac{e^{2}+a}{be^2} \) determine the value of \( a + b \).

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