a. From the Fundamental Theorem of Calculus, we have Use this fact to show that any function

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a. From the Fundamental Theorem of Calculus, we have

(6" = [xp6" []

Use this fact to show that any function y given by Equation (11.61) solves linear first-order Equation (11.55).

Equation 11.61

2 + xp (x)0 (x)m (x) y = [(x

Equation 11.55

y' + P(x)y= Q(x) (11.55)b. If the constant C is given by:

C = you()  [ u(t) Qa) dt - ox/

in Equation (11.61), show that the resulting function y defined by Equation (11.61) satisfies the initial condition y(x0) = y0.

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Related Book For  book-img-for-question

A First Course In Mathematical Modeling

ISBN: 9781285050904

5th Edition

Authors: Frank R. Giordano, William P. Fox, Steven B. Horton

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