I'm have some trouble understanding what my lecturer did.
The question is:
For the IVP, , , y(0)=1,
find an appropriate Lipschitz constant L in the domain . Hence determine whether or not the soln y(x) is unique.
We've found L = 1/2 (by finding and maximizing in our domain, but doesn't this function have a singularity at y=0? Which means the uniqueness thm doesn't apply?
Can someone explain?
EDIT: Also, he did things like:
y(0)=1 => (x+y)/2y > 0 => y' > 0
=> y increases
=> y >= 1
Which I don't understand.