Answer
$I(t)$ = $\frac{1}{10}(1-e^{-20t})$
Work Step by Step
$\frac{dI}{dt}+20I$ = $2$
$A(t)$ = $20$
$B(t)$ = $2$
$α(x)$ = $e^{20t}$
$(e^{20t}I)'$ = $2e^{20t}$
$e^{20t}I$ = $\frac{1}{10}e^{20t}+C$
$I(t)$ = $\frac{1}{10}+Ce^{-20t}$
$I(0)$ = $0$
$0$ = $\frac{1}{10}+C$
$C$ = $-\frac{1}{10}$
$I(t)$ = $\frac{1}{10}(1-e^{-20t})$