First order linear - substitution - why take the +ve square root?

Hi guys,

So the equation looks like this,

$\displaystyle \frac{dy}{dx} + \left(\frac{1}{2}\tan x \right)y = -(2\sec x)y^3,\,\,\,-\frac{\pi}{2}<x<\frac{\pi}{2}$

and we're required to use the substitution $\displaystyle z=y^{-2}$

Well I do it all and get to

$\displaystyle z = \frac{4x+c}{\cos x}\implies y^2 = \frac{\cos x}{4x+c}$

The answer in the back of the book takes the positive square root of this, and I can't see why. It would be easy to shrug it off, since I've done the hard part, but I really would like to know why the positive square root is taken, it's probably something simple I've missed (Wink)

Thanks

Stonehambey