I have the following nonlinear equations which I wish to express in terms of Lambert W functions.
$$bx^a\exp(cx)=y\tag{1}$$
$$ (1+x^c)^{-m}bx^a=y\tag{2}$$
where $x$ is the root in both equations.
Is it possible to obtain closed form for the root $x$ in both equations using Lambert W function?
Thank you.