This past semester, I just took an introductory course on G.R., which translates to a lot of differential geometry and then concluding with Schwarzschild's solution. We really didn't do any cosmology. However, one of the themes that kept creeping up again and again is that in 4-dimensions, Einstein's field equations are partial differential equations, that are coupled, and generally, very difficult to solve. So, I was all fine with that. However, searching on YouTube, I came across these "newer" lectures that now claim around 6:00 that Einstein's equations are ODEs. Further, the lecturer discusses solutions of them. Can anyone elaborate? Are they PDEs or ODEs?
The lecture can be found here: https://www.youtube.com/watch?v=SpCwDGKZKB0