I am trying to solve the following:
Let $x(t)$ be a solution of $x''=\frac{1}{x}$ satisfying $x(0)=1,x'(0)=2$. Let $t_0$ be the time when $x(t_0)=3$, find $x'(t_0)$.
I got that $x'(t_0)=\pm\sqrt{4+2ln(3)}$.
I believe I should take the $+$ sign solution, how can I argue that ? Help is appriciated!