Use the Fundamental Theorem of Calculus and the Product Rule to verify directly that for any x

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Use the Fundamental Theorem of Calculus and the Product Rule to verify directly that for any x0, the function

f(x) = a(x)- - Lane a(t)Q(t) dt

is a solution of the Initial Value Problem

y + P(x)y = Q(x), y(xo) = 0

where α(x) is an integrating factor [a solution to Eq. (3)].

da dx = a (x) P(x)

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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