a) How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(0)=y_0$ and $y'(0)=y_1$ $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}, t<0.$$ Here $n$ is an integer $>2$.

b) Can the previous equation have two different solution (with different initial conditions) in $(-2,-1)$, such that one is bounded and the second is not bounded?