I think I'm understanding better, but still not quite there yet. Please point out my mistakes (if any lol).

Find the general solution of the given differential:

dy/dt = [te^y]/(2t-1)

d/e^y (te^y) = d/dt 2t-1

integral d/e^y (te^y) d/dy = integral d/dy (2t-1) d/dt

integral e-y = 2 integral (t-1) dt

ln -[y] = 2/(t-1) + C