Step 1

\(xe^{y}=x-y\)

\(\Rightarrow\) Implicit diff

\(e^{y}+xe^{y}\frac{dy}{dx}=1-\frac{dy}{dx}\)

\(\Rightarrow xe^{y}\frac{dy}{dx}+\frac{dy}{dx}=1-e^{y}\)

\(\Rightarrow(xe^{y}+1)\frac{dy}{dx}=(1-e^{y})\)

\(\Rightarrow\frac{dy}{dx}=\frac{1-e^{y}}{xe^{y}+1}\)

\(xe^{y}=x-y\)

\(\Rightarrow\) Implicit diff

\(e^{y}+xe^{y}\frac{dy}{dx}=1-\frac{dy}{dx}\)

\(\Rightarrow xe^{y}\frac{dy}{dx}+\frac{dy}{dx}=1-e^{y}\)

\(\Rightarrow(xe^{y}+1)\frac{dy}{dx}=(1-e^{y})\)

\(\Rightarrow\frac{dy}{dx}=\frac{1-e^{y}}{xe^{y}+1}\)