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I am currently reading Liddles Introduction to Modern Cosmology (2nd Ed) and having trouble with problem 8.4, about the age of the universe with a cosmological constant.

The question asks to derive the formula for the age by first writing the Fridemann equation in such a model as

[itex]\frac{da}{dt}[/itex] = [itex]H^{2}_{0}[/itex] [itex][Ω_{0}a^{-1}[/itex] + [itex]\left(1-Ω_{0})a^{-2}\right][/itex]

But I'm not sure how this step is found, so can't proceed any further. I would appreciate any help to get me started.