Integrating Factors Example

(Section 2.1: Prob. 9)

y' - 2y = 3e^t

$$\mu(t) = e^{- \int{2 \: dt}} = e^{-2t}$$

e^-2t y' - 2e^-2t y = 3e^-t

[e^-2t y]' = 3e^-t

e^-2t y = -3 e^-t + c

y = -3 e^t + c e^2t