Chapter 8.1, Problem 15P

Consider the initial value problem

$\begin{array}{cc}y\text{'}=3t^2/(3y^2-4),& y(1)=0.\end{array}$

a) Use Euler’s method with $h=0.1$ to obtain approximate values of the solution at $t=1.2,1.4,1.6,\text{and}1.8$

b) Repeat part (a) with $h=0.05$.

c) Compare the results of parts (a) and (b). Note that they are reasonably close for $t=1.2,1.4,\text{and}1.6$ but are quite different for $t=1.8$. Also note (from the differential equation)that the line tangent to the solution is parallel to the $y-$ axis when $y=\pm 2/\sqrt{3}\cong \pm 1.155$. Explain how this might causesuch a difference in the calculated values.