Solve y - y = 0 for the initial conditions y(0) = 1, y'(0) = -1. Then
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Solve y" - y = 0 for the initial conditions y(0) = 1, y'(0) = -1. Then change the initial conditions to y(0) = 1.001, y' (0) = -0.999 and explain why this small change of 0.001 at t = 0 causes a large change later, e.g., 22 at t = 10. This is instability: a small initial difference in setting a quantity (a current, for instance) becomes larger and larger with time t. This is undesirable.
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