Chapter 8.4, Problem 19ES

(a) Use Euler’s Method with a step size of $\Delta x=0.2$ to approximate the solution of the initial-value problem

$y\text{'}=x+y,y(0)=1$ over the interval $0\le x\le 1.$

(b) Solve the initial-value problem exactly, and calculate the error and the percentage error in each of the approximations in part (a).

(c) Sketch the exact solution and the approximate solution together.