Is there a way to download youtube videos without any 3rd party software or websites like keepvid or whatever.?

Not really.

There's no way to use the source code to get the file itself. Youtube's media player, in software terms, is a 'black box', you don't know what's inside. In its own code (the source code is only the text version of the web page, not the code of any programs or modules run within it), it knows the location of all the actual files on Youtube's servers, but you can't see it, you can never gain access to the player's internals. When you try to load a video, a coded, but meaningless (to us) instruction is sent to that player. The player can interpret the request to produce the file you want to see.

So say you want to watch the classic 'Sittin on tha toilet'. The hyperlink, and the source code, say 'watch?v=BYW6C44zo24', that string after the '=' is the coded instruction sent to the player. The player knows which video that means, and knows the physical location of the video on Youtube's hardware, so it can stream it to you. But you never see the link of that location.

That's why third party things exist, like other sites or plugins. Since Youtube still has to stream that video's data to you, so you can see it, these sites or plugins intercept the data and allow it to be saved as a physical file. Browsers don't do that by default, and that's why the plugins exist, to modify the browser to let it do it.

So in short, either you can't, or you download a browser that already can do the above. But you couldn't do it manually unless you're the kind of person who could write those plugins in the first place.

(My explanation is simplistic, it's possibly way more complicated as they have some anti-downloading measures, that have to be defeated each time they update.)