Question:Solve the given differential equation:
\begin{equation*}
\frac{dy}{dx}=\frac{x-e^{-x}}{y+e^{y}}
\end{equation*}
Solution:
Reordering:
\begin{equation*}
(y+e^{y})dy=(x-e^{-x})dx
\end{equation*}
Take integration and multiplying$2$on both sides:
\begin{equation*}
y^2+2e^{y}=x^2+2e^{-x}+c
\end{equation*}
for $c$ being constant.
Reordering,get implicit solution
\begin{equation*}
y^2-x^2+2e^{y}-2e{-x}=c
\end{equation*}
