Can somebody help me solve r" = -C/(r^4) where c is a constant, and r" is the 2nd order dervative of r (wrt time)

THis is relating to a question: http://www.answerbag.com/q_view/1860951
I am trying to work out the time it takes for two magnets to snap together when placed distance r apart. Ive come this far, the equation in the question, but am rusty with my maths. I dont know whether Laplace transformation, Partial differentiation etc is needed. Ive tried to solve using an example as a model but get an answer with irrational numbers etc. The constant C above contains all the constants of the problem, magnetic dipoles, mass etc. Anybody on top of their maths please can you suggest best methid to solve?