If $\gamma(s) = \mathbf{x}(\gamma^1(s),\gamma^2(s))$ where $\mathbf{x}$ is a coordinate patch, then what is the differential equations that $\gamma^k$ ($k = 1,2$) must satisfy if $\gamma$ is a geodesic?
Note: A unit speed curve $\gamma(s)$ in $M$ is a geodesic iff $[n,T,T'] = 0.$