Hi!
My information is correct, for sure.
The OBJ format was designed as import and export format for 3D models.
Animation is not part of the original specification for this format and is NOT supported (in general).
In some cases developers enhance certain file formats and add custom features for their own products, but this breaks compatibility with other programs using this format.
In some cases there are also new specifications added to a certain file format and then there exist multiple versions like for FBX, where you can export as "FBX 2011" or "FBX 2018".
Technically it's possible to save every possible information into an ASCII or binary file, this is not a prove for a supported feature.
If you want to make sure that the data you save into a 3rd party format can be read by other applications you should stick to the most common used specifications/features.
If you want to export animation data into a single ASCII file with the extension .obj you need to create your own script / plug-in for Maya.
The questions is how and where do you want to read this data?
Maybe you need to create an importer too, for the application that needs to be able to read this file, or if this application already supports animation for OBJ, you need to adapt your Maya exporter to support the specifications of this implementation.