Differential equations help?

Question

Solve the initial value problem and determine how the interval in which the solution exists depends on the initial value C.

y' = -4t / y y(0) = C

Ok, i know how to solve this problem. Its just the other parts of the question that i dont get.

1. "determine how the interval on which the solution exists depends on the initial value C"
How do I find the interval??
How does the interval rely on the initial value C??

please help.

Answer 1

The solution is y^2 = -4*t^2 + C

or

y = sqrt(-2*t^2 + C)

For real solution, you cannot have the sqrt of a negative number, so the solution exists for C>=2*t^2