(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Second-order nonlinear ordinary differential equation

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