Here are some values of the solution that I got by starting with a low
value for Xfinal and slowly increasing:
(X ,Y)
(1 , 2)
(1.05,2.7)
(1.1,6)
(1.11, 11)
(1.112, 18)
(1.113, 31)
(1.1135,185)
(1.114.... calculator hourglass remains for longer than I care to
wait).
Note the independent variabel X points above are not equally spaced,
but getting closer together.
It seems pretty clear the solution blows up around 1.115.