How to solve equation $ x=W(a+bx^{n})+1 $? How i can resolve the equation $x=W(a+b x^n)+1$, where $W$ is the Lambert $W$ function?
thanks

I don't think it will be easy to solve. Since $x = W(y)$ if and only if $y \ge - \dfrac 1e$ and $y = xe^{x}$, you will have to solve $$a+bx^n = (x-1)e^{x-1},\quad a + bx^n \ge - \dfrac 1e.$$
Are you looking for an exact solution?
