I tried to do this in sage:
sage: de=-diff(y,x,2)-G*M/y^2
sage: desolve(de, y, ics=[0,1000])
But sage just says this:
TypeError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation may help (example of legal syntax is 'assume(%k1>0)', see assume?
for more details)
Is %k1 positive or negative?
But when I use assume(%k1>0) I get a syntax error, saying that there's something wrong with the percentage sign.