Chapter 6.4, Problem 1E

Apply the Midpoint Method for the IVPs

$\begin{array}{l}\text{a}\text{. }y\text{'}=t\\ \text{b}\text{. }y\text{'}=t^{2}y\\ \text{c}\text{. }y\text{'}=2(t+1)y\\ \text{d}\text{. }y\text{'}=5t^{4}y\\ \text{e}\text{. }y\text{'}=1/y^2\\ \text{f}\text{. }y\text{'}=t^3/y^2\end{array}$

with initial condition $y(0)=1$ . Using step size $h=1/4$, calculate the Midpoint Method approximation on the interval [0, 1]. Compare with the correct solution found in Exercise 6.1.3, and find the global truncation error at $t=1$.