Chapter 8.3, Problem 24P

In each of Problems 21 through 24, carry out one step of the Euler method and of the improved Euler method, using the step size $h=0.1$. Suppose that a local truncation error no

greater than $0.0025$ is required. Estimate the step size that isneeded for the Euler method to satisfy this requirement at the first step.

$\begin{array}{cc}y\text{'}=(y^2+2ty)/(3+t^2),& y(0)=0.5\end{array}$