How do I solve this differential equation:
$\displaystyle m\frac{d^2x(t)}{dt^2}=\frac{-c}{x(t)^2}$, c and m are constants larger than 0. Initial conditions are x(0)=a, x'(0)=0.
I don't understand something, if you have a harmonic oscilator differential equation:
x''(t)+a^2*x(t)=0,
the solution is:
x(t)=Acos(a*t)+Bsin(a*t).
So why don't you get solution x(t)? Or do you suggest that solution is:
x(t)=c1+c2*t+c/m*ln(t) ?
If so, I don't think that's a solution, try puting it in initial equation.