Well, it depends on what Sqrt (or ^(1/2)). In general there
are two square roots and in complex domain you can not
really separate them, one will analytically continue to
the other.
AFAICS the (C[1] - x)^2/x is better. With complex C[1]
writing E^(C[1]/2) is just obscure way of saying that we
have arbitrary nonzero constant. This is even more obscure
since replacing E^(C[1]/2) leads to valid solution. With
real C[1] writing constat as E^(C[1]/2) excludes negative
values and conseqently some solutions. And if you insist
that argument to Sqrt must be positive, then you get
restrictions on x anyway.
BTW: AFAICS 0 is singular solution, not covered by
formulas above. You can glue it with other solutions
at point where other solution is 0, so starting from
0 initial condition you get infintely many solutions.
--
Waldek Hebisch