Chapter 4.2, Problem 100E

Estimate the following solutions using Euler’s method with n = 5 steps over the interval t = [0, 1]. If you are able to solve the initial-value problem exactly, compare your solution with the exact solution. If you are unable to solve the initial-value problem, the exact solution will be provided for you to compare with Euler’s method. How accurate is Euler’s method?

100. y' = y²In(x + 1), y(0) = 1. Exact solution is $y=-\frac{1}{(x+1)(\text{In(x+1)-1})}$