Variation of parameters applied to y''-3y'+2y=e^x (Q1648)

y_{1}=e^{x},\\quad y_{2}=e^{2x},\\quad W=y_{1}y_{2}'-y_{2}y_{1}'=e^{3x};\\qquad u_{1}'=-\\frac{y_{2}\\,g}{W}=-1,\\quad u_{2}'=\\frac{y_{1}\\,g}{W}=e^{-x}