Suppose the function x(t) satisfies the initial value problem mx cx' kx F(t), x(a) bo, x'(a) b for ta and x(t) 0 for t a Then show that X(s) L x (t) satisfies the equation m (5 (eas X) sbo b) c(s(eas X) bo) k (eas X) L F(t a) ...

Suppose the function x(t) satisfies the initial value problem mx + cx' + kx = F(t), x(a)

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Suppose the function x(t) satisfies the initial value problem

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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Question Posted: Aug 11, 2023 01:49 PM

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Suppose the function x(t) satisfies the initial value problem mx + cx' + kx = F(t), x(a)

Question:

mx" + cx' + kx = F(t), x(a) = bo, x'(a) = b₁ for ta and x(t) = 0 for t < a. Then show that X(s) = L{x (t)} satisfies the equation m (5² (eas X) - sbo-b₁) + c(s(eas X) - bo) + k (eas X) = L{F(t + a)}.

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Differential Equations And Linear Algebra

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