For a positive constant $C$:
\begin{align}
y(x)+C\ln y(x)=f(x).
\end{align}


At least from specific $f(x)$, such as piece-wise linear function, is there an explicit solution for $y(x)$?



Does this equation have an explicit solution?
The solution can be expressed in terms of the Lambert W-function: according to Maple, $y(x) = e^{-W(e^{f(x)})+f(x)}$.


