Show that y(t) = 0 and are both solutions of the initial value problem , where y(0) = 0....

Show that y(t) = 0 and are both solutions of the initial value problem , where y(0) = 0. Explain why this fact does not contradict Theorem 7.16.

THEOREM 7.16 Uniqueness of solutions

Suppose the function f (t, x) and its partial derivative ∂f/∂x are both continuous on the rectangle R in the tx-plane. Suppose and that the solutions

Then as long as (t, x(t)) and (t, y(t)) stay in R, we have

x(t) = y(t).