# A Differential Equation

Calculus Level 2

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 $$a + b$$.

×