Chapter 9: First-Order Differential Equations - Practice Exercises - Page 557: 5

$(y+1)e^{-y}=-\ln |x| +c$

Need to separate the variables to determine the differential equation and then integrate the obtained equation on the both sides. $\int y(e^{-y}) dy=\int \dfrac{1}{x}dx$ This implies that $-y(e^{-y}) +\int (e^{-y}) dy=\ln |x| +c$ or, $-(y+1)(e^{-y})=\ln |x| +c$ so, $(y+1)e^{-y}=-\ln |x| +c$