Differential equations - solving initial value problem

[DWill]

1. The problem statement, all variables and given/known data
Solve the given initial value problem and determine how the interval in which the solution exists depends on the initial value y0.

y' = -4t/y, y(0) = y0


2. Relevant equations



3. The attempt at a solution
I solved the DE and got to:

y = +/- sqrt(C - 4t^2)

Plugging in y_0 for y when t = 0, I get:

y = +/- sqrt( (y_0)^2 - 4t^2 )

I'm pretty sure this is the right, but how do I answer the last part of the question? Figuring out the how the interval depends on initial value? thanks

[Hootenanny]

1. The problem statement, all variables and given/known data
Solve the given initial value problem and determine how the interval in which the solution exists depends on the initial value y0.

y' = -4t/y, y(0) = y0


2. Relevant equations



3. The attempt at a solution
I solved the DE and got to:

y = +/- sqrt(C - 4t^2)

Plugging in y_0 for y when t = 0, I get:

y = +/- sqrt( (y_0)^2 - 4t^2 )

I'm pretty sure this is the right, but how do I answer the last part of the question? Figuring out the how the interval depends on initial value? thanks
Usually, unless stated otherwise, one would assume that the solution must be real-valued.