Let x = x(t), y = y (t) be the solution of the initial-value problem Suppose that we
Chapter 4, Problem 10(choose chapter or problem)
Let \(x=x(t), y=y(t)\) be the solution of the initial-value problem
\(\frac{d x}{d t}=-x-y, \quad \frac{d y}{d t}=2 x-y, \quad x(0)-y(0)=1 .\)
Suppose that we make an error of magnitude \(10^{-4}\) in measuring \(x(0)\) and \(y(0)\). What is the largest error we make in evaluating \(x(t), y(t)\) for \(0\leqslant t<\infty\)?
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