A separable equation

Calculus Level 2

If dydx=ex+y\dfrac{dy}{dx}=e^{x+y}, and y(0)=0y(0)=0, then the value of y(ln2)y(-\ln 2) can be written in the form ln(mn)\ln \left(\dfrac mn\right), where mm and nn are coprime positive integers. Find m+nm+n.

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