Find the bifurcations (if any) and their type:

x'=x^3-sinh(x+ \mu^3)





So if we call that function f, I need f = f' = 0 right?


Well that gives me

x^3-sinh(x+\mu^3)=3x^2-cosh(x+\mu^3)=0

Some simple manipulation gives:

cosh(x+\mu^3)^3-27cosh(x+\mu^3)^2+27=0

What am I doing wrong? I cannot solve this.