Chapter 8.1, Problem 17P

Consider the initial value problem

$\begin{array}{cc}y\text{'}=(y^2+2ty)/(3+t^2),& y(1)=2.\end{array}$

Use Euler’s method with $h=0.1,0.05,0.025,\text{and}0.01$ toexplore the solution of this problem for $1\le t\le 3.$ What isyour best estimate of the value of the solution at $t=2.5$? At $t=3$? Are your results consistent with the direction field in Problem 10?