Given the geodesic equation
$$\ddot{x}^{\mu}+\Gamma^{\mu}_{\nu\lambda}\dot{x}^{\nu}\dot{x}^{\lambda} = 0$$ I wish to find a co-ordinate system around a point $x_0$ such that the geodesic equation reduces to $$\ddot{x}^{\mu} = 0$$ around $x_0$. Can anyone explain with steps how that maybe done? I am unable to find any systematic mathematical derivation of the above anywhere
