I'm an AP Calc teacher. A problem I gave my students states:

Find the general solution to the exact differential equation.

$\displaystyle y'=5 sec^2 x - 1.5 \sqrt x$

$\displaystyle y(0)=7$

So taking the anti derivative,

$\displaystyle y=5 tan x - x^{3/2} + 7$

That's fine. The solution also notes:

$\displaystyle (0 < x < \pi/2)$

Can anyone explain why this domain restriction is in place? I understand that there is a discontinuity at pi/2, but why does it choose this specific interval? Is it because the initial value is given at 0?

Thanks for any help.