Chapter 8.3, Problem 19P

In each of Problems 19 and 20, use the actual solution $\varphi (t)$ todetermine $e_{n+1}$ and a bound for $e_{n+1}$ at any step on $0\le t\le 1$ for the improved Euler method for the given initial valueproblem. Also obtain a bound for $e_1$ for $h=0.1$, and compare it with the similar estimate for the Euler method andwith the actual error using the improved Euler method.

$\begin{array}{cc}y\text{'}=2y-1,& y(0)=1\end{array}$