Chapter 10 - Introduction to Differential Equations - 10.4 First-Order Linear Equations - Exercises - Page 524: 35

$I(t)$ = $\frac{1}{10}(1-e^{-20t})$

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