I am trying to solve a transcendetal equation that has no analytical solution (AFAIK).
My question is how to find different branches of solutions with Maple. So far, Maple
only returns one particular solution.

To fix ideas, my equation is of the type,
x-a*(1-x)* exp(bx)+c=0
For suitable values of a and b this equation seems to have, at least, two solutions in
the real axis and I would expect it to have a numerable infinite of solutions in the
complex...

Hello,

Sorry if the question is too naïve: I'm new to Maple.

I want to find the solutions, both in the real line and in the complex plane, of the following transcendental equation:

x+s*exp(x * sigma)-mu-s=0

mu is positive (say mu=6) and I am interested in the case in which s is both positive and negative (say, s=1 and s=-1).
By plotting s*exp(x * sigma) vs. mu+s-x (x real), and also using fsolve, I can see that there are two solutions when s=1 ...