# Differential equations - solving initial value problem

## 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

## 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
Staff Emeritus
Gold Member

## 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

## 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.