Differential Equations with 1/x

[Derivitator]

Say you have a differential equation like this:

(1/y)dy = dx

When you integrate both sides, you get this:

ln|y| = x + C

Taking e to the both sides...

|y| = e^(x + C)

From here, my teacher says that the answer would simply be y = e^(x + C).
However, taking a simpler situation involving absolute values:

|y| = 1

In this case y = ±1.

1 is always positive, and so is e^(x + C).
So applying this to the above, I would get this instead:

y = ±e^(x + C)

Can anyone explain why the plus or minus is not (or is) needed?

[nona.m.nona]

You may find a useful discussion on page five of this PDF document.