With the initial conditions for a two mass system m1 and m2, where neither mass is significantly larger than the other, the resulting DE is unsolvable, right? Assume that they both start at rest:
(see DE below)
Do things get simpler if I give a starting velocity to both masses? What if I look at position relative to the com of the system?

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EDIT: last equation should be\[m_2\frac{d^2x_2}{dt^2}=\mp G\frac{m_1m_2}{(x_2-x_1)^2}\]

consider one of the mass to be at rest and another is accelerating.

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