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I would like to solve the following equation for $x$: $$ a= \left( \frac{x}{1-x} \right)^\lambda e^{bx} $$ I'm fairly new to using Lambert's W so I'm not sure if this is an appropriate tool for the problem.

David G. Stork
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econra2017
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1 Answers1

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After some simplifications the equation can be transformed into an equation of the form $A + B y = y e^y$ and I'm pretty sure that this equation can't be solved using the Lambert function (unless $A=0$ or $B=0$, of course).

I've solved many equations using the Lambert function and Mathematica always have been able to solve it too. For this one Mathematica wasn't able solve it.

jjagmath
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    I believe you are correct. Maple (which does well with the Lambert W function) does not solve $1+y=ye^y$. In the OP, the case $\lambda = 1, b=1$ is not solved by Maple. – GEdgar Aug 16 '21 at 19:59