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My calculus is really rusty and I need help solving this equation using a time derivative (denoted with a dot) in order to get the relativistic equation of motion for the Universe

The equation is:

adot^2 = Λc^2a^2/3

where adot is the time derivative of the scale factor, lambda is a cosmological constant, and c is the speed of light.

The answer should be:

a(t) = a(t0)e^Ht

where H is Hubble's constant = sqrt(c^2Λ/3)

But I don't know how to get there. Any help is appreciated!

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# Help me derive the relativistic equation of motion for the Universe

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