Chapter 6.6, Problem 1E

Using initial condition $y(0)=0$ and step size $h=1/4$, calculate the Backward Euler approximation on the interval [0, 1]. Find the error at $t=1$ by comparing with the correct solution found in Exercise 6.1.4.

$\begin{array}{l}\text{a}\text{. }y\text{'}=t+y\\ \text{b}\text{. }y\text{'}=t-y\\ \text{c}\text{. }y\text{'}=4t-2y\end{array}$