$[$Solve in computer$]$

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

alternative approaches:

$($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.

Question$2$ :The following ODE system is given $,$ where $y=y(x)$ and $z=z(x)$

$y^{\text{'}}+2y-4e^{-x}=0$

$z^{\text{'}}+\frac{y{z}^2}{3}=0$

At $x=0,$ the value of $y$ is given as $2,$ and the value of $z$ is given as $4.$ Solve the equation for the interval of $x=\left[\begin{array}{cc}0& 0\mathrm{.}3\end{array}\right]$ using Forward Euler's method with a stepsize of $0\mathrm{.}1.$