Converse of Picard’s Theorem Fails The conditions of Picard’s Theorem may fail at a given...

Converse of Picard’s Theorem Fails The conditions of Picard’s Theorem may fail at a given point for a differential equation, but the equation may still have a unique solution through the point. (In other words, the converse of Picard’s Theorem does not hold.)

(a) Show that the uniqueness condition for Picard’s Theorem does not apply to the differential equation

when y = 0.

(b) Find the general solution of the differential equation (5), and verify that the only solution with initial condition y(0) = 0 is y(t) ≡ 0, thus showing that negation of the hypothesis does not insure negation of the conclusion.