Consider the initial value problem

Hi everyone,

This is final time, so I am reviewing all chapters ready for final exam. I get 1 problem that I do not know how to figure out. Could you guys please help. I appreciate it.

Problem:

Consider the initial value problem: y' = 5.y^(4/5) ; y(1) = 0

Consider the two functions f1: R --> R and f2: R --> R such that

f1(x) ≡ 0 , f2(x) = (x -1)^5

a/ Show that f1 and f2 are both solutions to initial value problem.

b/ From part a, we see that the initial value problem has more than one solution. why does this not violate the statement of local existence and uniqueness theorem?