Flatness Problem Differential Equation

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gchmh
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Hello to everybody,

Since 3 days, I've been trying to obtain Eq. (173) from https://ned.ipac.caltech.edu/level5/Sept03/Trodden/Trodden5.html

I know I need to derivate with respect to a, but it is being impossible to obtain the final answer. Can anybody help me with a detailed derivation?

Thank you in a advance
 

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