Optimal path to swim across river in least time - Math Puzzle (HARD)

Another related math puzzle:
https://www.youtube.com/watch?v=fV_ZmSlJQbk

Both MATLAB scripts can be found here:
https://github.com/virtuallypassedsmartsparrow/Math-Puzzles

#SoME1

0:00 - Introduction
0:29 - Speeds
1:23 - Total time
1:47 - Constraint
2:37 - Euler Lagrange
4:20 - Solution
5:05 - MATLAB solution
5:42 - MATLAB solution using solver

Видео Optimal path to swim across river in least time - Math Puzzle (HARD) канала Virtually Passed