The question is broken down into two parts: a) find y in terms of x if with the initial conditions of y(0)=8 and b) for what x-interval is the solution defined?

dx/dy=(x^4)/(y^7)

For a) I have found it to be:

((8/5)x^5+8^8)^(1/8), which is correct.

But for b) its stated as a number _______<x< infinity (which i found). So what I need help with, is how do I determine the number for the first part of the interval.

Thanks.