6.2.2 Consider the system . a) Let D be the open disk x2 + y2 < 4. Verify that the system satisfies the hypotheses of the existence and uniqueness theorem throughout the domain D. b) By substitution, show that x(t) = sin t, y(t) = cos t is an exact solution of the system. c) Now consider a different solution, in this case starting from the initial condition . Without doing any calculations, explain why this solution must satisfy x(t)2 + y(t)2 < 1 for all t < .