Calculus (3rd Edition)

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

Chapter 10 - Introduction to Differential Equations - 10.4 First-Order Linear Equations - Exercises - Page 524: 38

Answer

$I$ = $\frac{1}{25}cos(80)+Ce^{-125t}$

Work Step by Step

$\frac{dI}{dt}+125I$ = $5cos(80t)$ $A(t)$ = $125$ $B(t)$ = $5cos(80t)$ $α(t)$ = $e^{125t}$ $(e^{125t}I)'$ = $5e^{125t}cos(80t)$ $e^{125t}I$ = $\frac{1}{25}e^{125t}cos(80)+C$ $I$ = $\frac{1}{25}cos(80)+Ce^{-125t}$
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