Chapter 8.3, Problem 12P

In each of Problem 7 through 12, find approximate value of the solution of the given initial value problem at $t=0.5,1.0,1.5,\text{and2}\text{.0}$.

a) Use the improved Euler method with $h=0.025$.

b) Use the improved Euler method with $h=0.0125$.

c) Use the Runge-Kutta method with $h=0.1$.

d) Use the Runge-Kutta method with $h=0.05$.

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