Off the top of my head, I'd say you would have to ask the concept or Relativity whether or not the relative acceleration is constant. Personally, I'd be a bit shocked if it were constant.
Since the position of Y is dependent on the position of X, we also have: (Which you might have stated in a less abbrevaited preamble.)
This leads nicely to the implicit derivatives:
Then, just a little algebra produces:
Frankly, this is a bit astounding. As X gets close to the Origin, the crew on Y had better batten down the hatches! If X only flinches, Y will jolt off a very long way... One cannot argue much with that SQUARED Dx in the denomiator. Wow!
Remember from the Special Theory of Relativity? It HAD to be astounding just how much energy differential would be created by a very small amount of converted matter. Same thing. Giant numbers in the numerator or tiny numbers in the denominator are bad enough. SQUARE them and forget it. That's BIG!