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 $y(x)$?


closed as off-topic by Neil Strickland, Gerald Edgar, abx, RP_, coudy Apr 11 '17 at 19:28

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

  • $\begingroup$ Sorry, could you help solve the revised more general form? Thanks. $\endgroup$ – Jay Apr 11 '17 at 16:16
  • $\begingroup$ I got it. It can be transformed back, and then use your solution. $\endgroup$ – Jay Apr 11 '17 at 16:23

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