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?