Find a particular solution of the differential equation $(x+1)\frac{dy}{dx}=2e^{-y} -1$, given that $y = 0$ when $x = 0$.

Question

$\begin{array}{1 1}y=\log\frac{|2x+1|}{|x-1|} \\y=\log\frac{|2x-1|}{|x+1|} \\ y=\log\large\frac{|2x+1|}{|x+1|} \\y=\log\large\frac{|2x-1|}{|x-1|} \end{array}$