Solving equation over iterative bounds when equation contains trig functions

I am trying to solve an equation for a variable that is within trig functions.. eg something like 5 - y = 1/(sinh(2x) + cosh(3x)); Where y is equal to say 1:500 and I am attempting to find all solutions of x and then select max/min x. Any suggestions? I am not very familiar using solver in Matlab. Thanks!

[John D'Errico]

Those are not trig functions of course.

So is your question about trig functions, or some other set of special functions, or ANY functions in general? The answer to my question would likely impact the answer to yours.

[Walter Roberson]

x = ln(root((-5+y)*z^6+(-5+y)*z^5+2*z^3+(5-y)*z-5+y),z)

That is, you find the 6 roots of the polynomial in z and take their logs and those are the y values. You would expect most of them to be complex.

When y = 5 then this degenerates and you get a log(0) -- looks like there is no solution there. But as y approaches 5 then there are solutions with component that approaches -infinity