Chapter 2.7, Problem 15P

(a)

To determine

The approximate values of the solution of initial value problem $y^{\prime }=\frac{3t^2}{\left(3y^2-4\right)},y\left(1\right)=0$ using Euler method with $h=0.1$ at $t=1.2,\text{ 1}\text{.4, 1}\text{.4, and 1}\text{.8}$.

(b)

To determine

The approximate values of the solution of initial value problem $y^{\prime }=\frac{3t^2}{\left(3y^2-4\right)},y\left(1\right)=0$ using Euler method with $h=0.05$ at $t=1.2,\text{ 1}\text{.4, 1}\text{.4, and 1}\text{.8}$.

(c)

To determine

To compare: The results obtained in part (a) and (b) and explain the reason for the difference in the calculated values when tangent line to the solution is parallel to y axis.