Hi again. Here's one.

(a) Without solving, explain why the intitial value problem

has no solution for .

(b) Solve the initial value problem in part (a) for and find the largest interval on which the solution is defined.

My attempt:

(a) Because the only way to arrive at a radical through differentiation is to begin with one, and any expression involving a radical (even root) with nothing outside of the radical must always give a positive result over the reals.

(b) I get

.

If I set , I get .

But, I won't evfen attempt to find the interval of definition because the book doesn't include the plus or minus. They have .

What's the deal here?