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Problem # 2. Consider the system of equations :i: = y g = 162:]! with initial condition 17(0) 2 0, y(0) = 1. Let :1:

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Problem # 2. Consider the system of equations :i: = y g = 162:]! with initial condition 17(0) 2 0, y(0) = 1. Let :1: = q5(t, is) denote the solution with this initial condition. (a) Find the derivative with respect to parameter k. (b) Does the derivative exist at k = 0? If yes, nd What is the value of 6% %(t=1,k=0)

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