Chapter 1.6, Problem 21P

In Problems $16-21$, solve the given initial-value problem.

$y^{\prime }-2y=f\left(x\right),y\left(0\right)=1$, where

$f\left(x\right)=\{\begin{array}{l}1-x,\text{if}x<\text{1,}\\ \text{0,}\text{if}x\ge 1.\end{array}$