well, it is a problem because Safari don't recognize login button on home page of udemy

propably JS error
Try hovering in the right hand corner , it will then appear.
Just had the same issue in Safari.
I also had a certificate error .
Since I have courses on udemy also , just tried with TFF , Safari and Webkit but indeed either you got to fake being a mobile device or find a way to play Flash files ( which is outdated on 10.4/10.5 )
[doublepost=1481660168][/doublepost]I found here that you would be able to choose in your preferences between
Flash and HTML5 but I don't have that option ? ( see Fixes 3. )
http://www.ghacks.net/2014/12/02/fix-udemy-videos-not-loading/
Do you get that option in your udemy profile preferences ?
Will try on my MBP Retina to see if I can switch the setting there.
No luck on El Capitan neither to switch the video preference