Chapter 2.3, Problem 38E

In Problems 37‒40 proceed as in Example 6 to solve the given initial-value problem. Use a graphing utility to graph the continuous function y(x).

38. $\frac{dy}{dx}+y=f(x)$, y(0) = 1, where

$f\left(x\right)=\{\begin{array}{l}1,\text{ 0}\le x\le \text{1}\\ -1,x\text{ >1}\end{array}$