Explanation Given: The differential equation is y ′ ( t ) = − 3 y + 9 with the initial point y ( 0 ) = 4 . Calculation: From the given differential equation, d y d t = − 3 y + 9 d y − 3 y + 9 = d t Integrate on both sides, ∫ d y − 3 y + 9 = ∫ d t − 1 3 ∫ 3 d y y − 3 = ∫ d t − 1 3 ln ( y − 3 ) = t + c ln ( y − 3 ) = − 3 t − 3 c Take exponential both sides, e ln ( y − 3 ) = e − 3 t − 3 c ( y − 3 ) = e − 3 c e − 3 t y ( t ) = C e − 3 t + 3 Where C = e − 3 c is a constant

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter D1, Problem 12RE

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To solve: The initial value problem of the given differential equation.

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Chapter D1 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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The initial value problem of the given differential equation.

Solution Summary: The author explains how to solve the initial value problem of the given differential equation.