The reaction system

$A+BC(desired)$

$A+BD(undesired)$

Can be represented by the system of differential equations

$\frac{d{C}_A}{dt}=-k_{1A}{C}_A{C}_B-k_{2A}{C}_A^{0\mathrm{.}5}{C}_B^{1\mathrm{.}5}$

$\frac{d{C}_B}{dt}=-k_{1A}{C}_A{C}_B-k_{2A}{C}_A^{0\mathrm{.}5}{C}_B^{1\mathrm{.}5}$

$\frac{d{C}_C}{dt}=k_{1A}{C}_A{C}_B,$

$\frac{d{C}_D}{dt}=k_{2A}{C}_A^{0\mathrm{.}5}{C}_B^{1\mathrm{.}5}$

$,k_1=1\mathrm{.}1{10}^7$exp$(-\frac{9200}{(T)}),k_2=4$exp$(-\frac{2000}{(T)})$

$C_{A0}=1,C_{B0}=1,C_{C0}=0,C_{D0}=0,T=500K$

On the same graph, plot the graph of yield $(Y)$ and selectivity$($S$)$ of compound $D$ with time

For the purposes of these calculations

$Y=\frac{C_C}{C_{A0}}$

$S=\frac{C_C}{C_D+e}$

$e={10}^{-20}.\%$ Define the time range

tr $=$ linspace$(0,100,50)$; $\%$Time points from $0$ to $100$ with $50$ intervals

$\%$ Initial concentrations

co $=[1,1,0,0]$; $\%$ Initial concentrations of Ca$,$Cb$,$Cc$,$Cd

$\%$Solve the ODE's

$[$t$,$c$]=$ ode$45($@hughes,tr$,$co$)$;

$\%$ Calculate Yield and Selectivity

Y $=$ c$($:$,3)./$co$(1)$; $\%$ Yield of c relative to initial A

e $=1$e$-20$; $\%$Small number to avoid division by zero

S$=$ c$($:$,3)./($c$($:$,4)+$e$)$; $\%$Selectivity of C over D

$\%$ Plot the results

plot$($t$,$Y$,$t$,$S$,$"linewidth",$2)$;

xlabel$(\text{'}$Time T$($s$)\text{'})$;

ylabel$(\text{'}$values$\text{'})$;

legend$("$Yield $($Y$)",$"Selectivity $($S$)")$;

title$("$Yield and Selectivity vs Time"$)$;

grid on;

$\%$ Define the ODE function

function dcdt $=$ hughes$($t$,$c$)$

T$=500$;

k$1=1\mathrm{.}1*10^7*$exp$(-9200/$T$)$;

k$2=4*$ exp$(-2000/$T$)$;

$\%$ Extract the concentrations from c

ca$=$c$(1)$; cb$=$c$(2)$; cc$=$c$(3)$; cd$=$c$(4)$;

dcdt $=[-$k$1*$ca$*$cb $-$k$2*$ca$^0\mathrm{.}5*$cb$^1\mathrm{.}5$;

$-$k$1*$ca$*$cb $-$k$2*$ca$^0\mathrm{.}5*$cb$^1\mathrm{.}5$;

k$1*$ca$*$cb;

k$2*$ca$^0\mathrm{.}5*$cb$^1\mathrm{.}5$

$]$;

end. I wrote this code in matlab for the problem above but I get this errors Error using vertcat

Dimensions of arrays being concatenated are not consistent.

Error in Multiple$\_$react$\_$tut$1>$hughes $($line $31)$

dcdt $=[-$k$1*$ca$*$cb $-$k$2*$ca$^0\mathrm{.}5*$cb$^1\mathrm{.}5$;

Error in odearguments $($line $90)$

f$0=$ feval$($ode$,$t$0,$y$0,$args$\{$:$\})$; $\%$ ODE$15$I sets args$\{1\}$ to yp$0.$

Error in ode$45($line $115)$

odearguments$($FcnHandlesUsed$,$ solver$\_$name, ode, tspan, y$0,$ options, varargin$)$;

Error in Multiple$\_$react$\_$tut$1($line $9)$

$[$t$,$c$]=$ ode$45($@hughes,tr$,$co$)$; when I run it$.$ Please check the question and debug my code for me