$[$

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

$=$

$0$

$.$

$5$

$.$

$$Use two different step sizes, and plot x

versus y graph for each case. The step sizes to be used are:

$($

a

$)$

$0$

$.$

$1$

$,$

$($

b

$)$

$0$

$.$

$0$

$1$

$.$

$$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

$)$

$0$

$.$

$1$

$,$

$($

b

$)$

$0$

$.$

$0$

$1$

$.$

$$Do you see any differences in the graphs? Compare your results with the graphs

you obtained with the Forward Euler method