Chapter 8.2, Problem 22P

Using a step size $h=0.05$ and the Euler method, butretaining only three digits throughout the computations, determine approximate values of the solution at $t=0.1,0.2,0.3,$ and $0.4$ for each of the following initial value problems

a) $\begin{array}{cc}y\text{'}=1-t+4y,& y(0)=1\end{array}$

b) $\begin{array}{cc}y\text{'}=3+t-y,& y(0)=1\end{array}$

c) $\begin{array}{cc}y\text{'}=2y-3t,& y(0)=1\end{array}$ $$

Compare the results with those obtained in Example 1 andin Problems 1 and 3. The small differences between some ofthose results rounded to three digits and the present results are due to round-off error. The round-off error would becomeimportant if the computation required many steps.