A Differential Equation

Calculus Level 2

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

If the value of y(2) y(2) can be written in the form e2+abe2 \dfrac{e^{2}+a}{be^2} determine the value of a+b a + b .

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