at pi/2 you would be dividing by 0 in the differential equation.

I'd think, since an initial condition is given at 0, that the actual domain is [0, pi/2)

You could choose any domain that includes zero and doesn't include (k+1/2)pi, k an integer, and those are

(-pi/2, 0], and [0, pi/2), however you also have a square root of x in your diff eq. That rules out the first interval if you are working on the real numbers.

So that leaves you only with [0,pi/2)