Let z\(t) and zi(t) be two complex-valued solutions of the initial value problemdz = kz
Chapter 9, Problem 38(choose chapter or problem)
Let z\(t) and zi(t) be two complex-valued solutions of the initial value problemdz = kz, dtwith z(0) = l.where A. is a complex number. Suppose that Z 2(t) ^ 0 for all /. a. Using the quotient rule (Exercise 37), show that the derivative of z\(t) zi(t) is zero. Conclude that zi(t) = Z2(t) for all /. b. Show that the initial value problem -X at with ^(O) = 1,has a unique complex-valued solution z(t). Hint: One solution is given in the text.
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