Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved, in

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Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved, in principle, by defining the integrating factor p(t) = exp(∫ a(t) dt). Here is how the integrating factor works. Multiply both sides of the equation by p (which is always positive) and show that the left side becomes an exact derivative. Therefore, the equation becomes


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Now integrate both sides of the equation with respect to t to obtain the solution. Use this method to solve the following initial value problems. Begin by computing the required integrating factor.image

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Calculus For Scientists And Engineers Early Transcendentals

ISBN: 9780321849212

1st Edition

Authors: William L Briggs, Bernard Gillett, Bill L Briggs, Lyle Cochran

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