Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.6 Models Involving y'=k(y-b) - Exercises - Page 360: 3


$$y=-6+11 e^{4t}$$

Work Step by Step

The general solution of $y'=4y+24=4(y+6)$ is $$y=-6+c e^{4t}.$$ When $y(0)=5$, then $5=-6+c$, i.e. $c=5+6=11$. Thus: $$y=-6+11 e^{4t}$$
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