Consider the equation x' = (x – 1) cos t.
(a) Let x(t) and y(t) be two solutions. What is the upper bound on the separation |x(t) – y(t)| predicted by Theorem?
(b) Find the solution x(t) with initial value x(0) = 0, and the solution y(t) with initial value y(0) = 1/10. Does the separation x(t) – y(t) satisfy the inequality found in part (a)?
(c) Are there any values of t where the separation achieves the maximum predicted?
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