Chapter 8.1, Problem 2P

In each of Problems 1 through 4:

a) Find approximate values of the solution of the given initial value problem at $t=0.1,0.2,0.3,\text{and}0.4$ using the Euler method with $h=0.1$.

b) Repeat part (a) with $h=0.05$. Compare the results with those found in (a).

c) Repeat part (a) wit $h=0.025$. Compare the results with those found in (a) and (b).

d) Find the solution $y=\varphi (t)$ of the given problem and evaluate $\varphi (t)$ at $t=0.1,0.2,0.3,\text{and}0.4$. Compare these values with the results of (a), (b), and (c)

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