Question

can some one explain this solution???

Question:
Determine the largets interval I of definition for the solution of the first order initial value problem
y'=y^2, y(0)=0

one parameter family of sol'n: y= - 1/(x+c)

Answer 1

obviousle if you plug in the initial values

0=-1/c

Answer 2

my question is why is the interval in the answer I ( - infinity , infinity)