Y(e^x +1)dy-e^x dx=0

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To solve this differential equation, we can start by rearranging the terms:

e^x dy - e^x dx = -dy
dy/dx = -1

Integrating both sides with respect to x:

∫ dy = ∫ -dx
y = -x + C

Therefore, the solution to the differential equation is y = -x + C, where C is the constant of integration.