(be sure to follow JPH feedback above about the proper ffmpeg download) Not sure why, but in my case here is the one that worked (in my case was on windows).
Initialize a writer:
import matplotlib.pyplot as plt
import matplotlib.animation as animation
Writer = animation.FFMpegWriter(fps=30, codec='libx264') #or
Writer = animation.FFMpegWriter(fps=20, metadata=dict(artist='Me'), bitrate=1800) ==> This is WORKED FINE ^_^
Writer = animation.writers['ffmpeg'] ==> GIVES ERROR ""RuntimeError: Requested MovieWriter (ffmpeg) not available""