I am studying ODE and I just started learning about second order ODE.
The question I'm trying to solve is somewhat of a physics problem (but a very simple physics, the hard part is the ODE involved). It is $x'' = \frac{1}{3x}.$
Considering $x(t)$ as the distance between two bodies ($x'(t)$ is the velocity) I am giving the initial conditions : $x(0)=4,x'(0)=v(0)=-2$.
I whish to find the value of $x(t)$ s.t $x'(t)=0$ (i.e where $v(t)=0$) and when does this happen (i.e find t s.t $v(t)=0$).
I would appriciate any help on this, I didn't really try anything because I don't know how to proceed.