Solved: Let X(t) be a fundamental matrix for the system x = A(t)x(t), where A(t) is an

Chapter 9, Problem 10

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Let X(t) be a fundamental matrix for the system x = A(t)x(t), where A(t) is an nn matrix function. Show that the solution to the initial-value problem x (t) = A(t)x(t) + b(t), x(t0) = x0 can be written as x(t) = X(t)X1(t0)x0 + X(t) t t0 X1(s)b(s)ds.

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