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: 4


$$y= 2+8 e^{-6t+12}.$$

Work Step by Step

Since $y'+6y=12 \Longrightarrow y'=-6(y-2)$ then the general solution is $$y=2+c e^{-6t}.$$ When $y(2)=10$, then $10=2+ce^{-12}$, i.e. $c=8e^{12}$. In this case $$y=2+8e^{12} e^{-6t}=2+8 e^{-6t+12}.$$
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