Assignment:
Q1. Find a Lipschitz constant, K, for the function f (u, t) = u^3 + t u^2 which shows that f is Lipschitz in u on the set 0 ≤ u ≤ 2, 0 ≤ t ≤ 1.
Q2. Show that the function f (u, t) = t u^(1/2), is not Lipschitz in u on [0, 1] × [0, 2].
Q3. Find two solutions to the initial value problem y, = |y|^(1/2) , y(0) = 0. What hypothesis of the Picard-Lindelöf Theorem is violated?
Provide complete and step by step solution for the question and show calculations and use formulas.