Chapter 1.5, Problem 11E

Consider the differential equation
   $\frac{dy}{dt}=\frac{y}{t^2}$
(a) Show that the constant function y₁(t) = 0 is a solution.
(b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when $t\le 0$ ,but that are non zero when t> 0. [Hint: You need to define the solutions using language like “y(t) = ... when $t\le 0$ and y(t) = ... when t>0.”]
(c) Why doesn’t this example contradict the Uniqueness Theorem?