Chapter 8.1, Problem 16P

Consider the initial value problem

$\begin{array}{cc}y\text{'}=t^2+y^2,& y(0)=1.\end{array}$

Use Euler’s method with $h=0.1,0.05,0.025,\text{and}0.01$ toexplore the solution of this problem for $0\le t\le 1.$ What isyour best estimate of the value of the solution at $t=0.8$? At $t=1$? Are your results consistent with the direction field in Problem 9?