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