How to solve Lambert W function?

[stevengj]

@Luigi_Marongiu

This is in the form
y = x exp(a(1−x/k))
From this post looks like the solution is not so straightforward since it requires to solve the Lambert function W.

To solve this for x, rewrite it as -ae^{-a} y/k = (-ax/k) e^{-ax/k}. Then -ax/k = \mathrm{W}(-ae^{-a} y/k) where \mathrm{W} is the Lambert W function, so x = -(k/a)\mathrm{W}(-ae^{-a} y/k).

In Julia with the LambertW.jl package, for example, x = -(k/a)*lambertw(-a*exp(-a)*y/k).