$[$Solve in computer$]$

For Question $(2),$ use a programming language $($python or R$)$ to solve for this question in two

alternative approaches:

$($a$)$ Use for loops and Forward Euler$$s method formula. You code will use the Forward Euler formula

to evaluate yi$+1$ within the loops between x$0=0$ to xfinal $=0\mathrm{.}5.$ Use two different step sizes, and plot x

versus y graph for each case. The step sizes to be used are: $($a$)0\mathrm{.}1,($b$)0\mathrm{.}01.$ Do you see any differences

in the graphs?

$($b$)$ Solve by using the $4$th order Runge$-$Kutta solver functions available in python or R$.$ Plot x versus y

graph. Use two different step sizes, and plot x versus y graph for each case. The step sizes to be used

are: $($a$)0\mathrm{.}1,($b$)0\mathrm{.}01.$ Do you see any differences in the graphs? Compare your results with the graphs

you obtained with the Forward Euler method