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**1. Homework Statement**

By substituting in

[tex]\left( \frac{\dot{a}}{a_0} \right)^2 = H^2_0 \left(\Omega_0 \frac{a_0}{a} + 1 - \Omega_0 \right)[/tex]

show that the parametric open solution given by

[tex]a(\psi)=a_0 \frac{\Omega_0}{2(1-\Omega_0)}(\cosh{\psi} - 1)[/tex]

and

[tex]t(\psi)=\frac{1}{2H_0} \frac{\Omega_0}{(1 - \Omega_0)^{3/2}}(\sinh{\psi} - \psi)[/tex]

solve the Friedmann equation.

**2. The attempt at a solution**

I get

[tex]\dot{a} = a_0 \frac{\Omega_0}{2(1 - \Omega_0)}(\dot{\psi}\sinh{\psi})[/tex]

and

[tex]\dot{\psi}=\frac{2H_0(1-\Omega_0)^{3/2}}{\Omega_0(\cosh{\psi}-1)}[/tex]

but I can't get to the first equality. Is this the correct approach?