Chapter 6.1, Problem 10CP

Calculate the Euler’s Method approximate solution of the differential equation $y\text{'}=\sinh y$ and initial condition (a) $y_0=1/4$ on the interval [0, 2] (b) $y_0=2$ on the interval [0, 1 /4], using step sizes $h=0.1\times 2^{-k}$

for $0\le k\le 5$

. Plot the $k=0$ and $k=5$

approximate solutions along with the exact solution (see Exercise 16), and make a log-log plot of the error at the end of the time interval as a function of h.