I have tried and tried but cannot for the life of me see how one equation follows onto the other... can anybody help??
$$\Omega(\theta)=-b.\coth(\operatorname{arsinh}(\exp a\theta . \sinh(c_0)))$$
$$\implies \Omega(\theta)=\sqrt(c_1.\exp -2a\theta + b^2)$$
Note that: $$C_0=-\operatorname{arcoth}\left(\frac{\Omega_0}{b}\right)$$
Eichberger quotes (at the bottom of page 5) "By inserting (11) into (8), using identities of the hyperbolic transcendental functions and carefully observing ± signs, we obtain Ω as a function of θ."