I urgentely need help with this matlab problem. I have attached my current code. What is wrong with it$?$ It says that the outuput variables have the wrong values.

The deflection $y$ of a sailboat mast subjected to a wind force can be modeled with the following differential equation:

$\frac{d^{2}y}{d{z}^2}=\frac{f(z)}{2EI}(L-z{)}^2$

where $z$ is the position along the mast starting from $0$ at the base. The function $f(z)$ is the force of the wind transferred to the mast by the sail and can be modeled as

$f(z)=\frac{200z}{5+z}{e}^{\frac{-2z}{30}}$

parameter $L$ is the length of the mast.

Write a MATLAB function P$2\_$odesolve that will solve for deflection $y(z)$ and the slope $\frac{dy}{dz}$ given that the deflection and the slope are both equal to $0$ at the base of the mast with the following outputs $($in given order$)$:

Solutions using Euler's method as a $2-$column matrix $($store solution for deflection $y(z)$ in the first column and the solution for slope $\frac{dy}{dz}$ in the second column$)$

Solutions using Heun's method $($without corrector iteration$)$ as a $2-$column matrix $($store solution for deflection $y(z)$ in the first column and the solution for slope $\frac{dy}{dz}$ in the second column$)$

Solutions using Midpoint method as a $2-$column matrix $($store solution for deflection $y(z)$ in the first column and the solution for slope $\frac{dy}{dz}$ in the second column$)$

with the following input

vector defining the span of the mast with intial and final position values $(12$ row vector$)$

initial value vector for the deflection and the slope $(12$ row vector$)$

solver step size $h($scalar$)$ Function $($

$1$ function $[yE,yH,yM]=P2$ odesolve$($zspan$,y0,h)$

$2\%$type your code below, do not change the name of the function and the order of the variables$\%$

Code to call your function $(8)$

Current code:function $[$yE$,$ yH$,$ yM$]=$ P$2\_$odesolve$($zspan$,$ y$0,$ h$)$

$\%$ Constants

E $=1\mathrm{.}3$e$8$;

I $=0\mathrm{.}05$;

L $=$ zspan$(2)-$ zspan$(1)$;

$\%$ Number of steps

N $=$ round$(($zspan$(2)-$ zspan$(1))/$ h$)$;

$\%$ Initialize solution matrices

yE $=$ zeros$($N$+1,2)$;

yH $=$ zeros$($N$+1,2)$;

yM $=$ zeros$($N$+1,2)$;

$\%$ Initial conditions

yE$(1,$ :) $=$ y$0$;

yH$(1,$ :) $=$ y$0$;

yM$(1,$ :) $=$ y$0$;

$\%$ Function for f$($z$)$

f $=$ @$($z$)200*$ z$^5+$ z $*$ exp$(-2*$ z $/30)$;

$\%$ Euler's Method

for n $=1$:N

z $=$ zspan$(1)+($n$-1)*$ h;

y $=$ yE$($n$,1)$;

v $=$ yE$($n$,2)$;

yE$($n$+1,1)=$ y $+$ h $*$ v;

yE$($n$+1,2)=$ v $+$ h $*($f$($z$)/(2*$ E $*$ I $*($L $-$ z$)^2))$;

end

$\%$ Heun's Method

for n $=1$:N

z $=$ zspan$(1)+($n$-1)*$ h;

y $=$ yH$($n$,1)$;

v $=$ yH$($n$,2)$;

$\%$ Predictor step

y$\_$star $=$ y $+$ h $*$ v;

v$\_$star $=$ v $+$ h $*($f$($z$)/(2*$ E $*$ I $*($L $-$ z$)^2))$;

$\%$ Corrector step

yH$($n$+1,1)=$ y $+($h $/2)*($v $+$ v$\_$star$)$;

yH$($n$+1,2)=$ v $+($h $/2)*(($f$($z$)/(2*$ E $*$ I $*($L $-$ z$)^2))+($f$($z $+$ h$)/(2*$ E $*$ I $*($L $-($z $+$ h$))^2)))$;

end

$\%$ Midpoint Method

for n $=1$:N

z $=$ zspan$(1)+($n$-1)*$ h;

y $=$ yM$($n$,1)$;

v $=$ yM$($n$,2)$;

$\%$ Midpoint step

y$\_$mid $=$ y $+($h $/2)*$ v;

v$\_$mid $=$ v $+($h $/2)*($f$($z$)/(2*$ E $*$ I $*($L $-$ z$)^2))$;

$\%$ Full step

yM$($n$+1,1)=$ y $+$ h $*$ v$\_$mid;

yM$($n$+1,2)=$ v $+$ h $*($f$($z $+$ h $/2)/(2*$ E $*$ I $*($L $-($z $+$ h $/2))^2))$;

end

end Pretest results are not submitted for grading. To run all the tests and submit the results for grading, click Submit.

Is the solution computed using Euler's method correct using values from the example? $($Pretest$)$

Variable yE has an incorrect value.

Is the solution computed using Heun's method correct using values from the example? $($Pretest$)$

Variable $yH$ has an incorrect value.

Is the solution computed using Midpoint method correct using values from the example? $($Pretest$)$

Variable $yM$ has an incorrect value.