1. The problem statement, all variables and given/known data Given the Second-order nonlinear ordinary differential equation x''(t)=1/(x(t)^2) Find x(t). 2. Relevant equations I tried use Laplace transforms, and solving it using linear methods but that is not useful. 3. The attempt at a solution I tried to find t(x) and got to dt=dx/((C-2GM/x)^0.5) or something like that. I guess you could find t(x) then find [inverse t(x)] = x(t) But I would like to know how to solve it properly really.