Find the bifurcations (if any) and their type:
$\displaystyle x'=x^3-sinh(x+ \mu^3)$
So if we call that function f, I need f = f' = 0 right?
Well that gives me
$\displaystyle x^3-sinh(x+\mu^3)=3x^2-cosh(x+\mu^3)=0$
Some simple manipulation gives:
$\displaystyle cosh(x+\mu^3)^3-27cosh(x+\mu^3)^2+27=0$
What am I doing wrong? I cannot solve this.