Differential equations - solving initial value problem

[DWill]

Homework Statement

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

Homework Equations

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]

Homework Statement

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

Homework Equations

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.