Show me the step to solve this coding problem in mathlab using some of code we have draft here and please help me solve it$.\%\%$ Clear Cache

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$\%\%$ Predator Prey Problem

$\%$ Define the Lotka$-$Volterra coefficient

a $=0\mathrm{.}65$; b $=0\mathrm{.}04$;

c $=0\mathrm{.}32$; d $=0\mathrm{.}05$;

$\%$ Set the time$-$stepping parameters

tf $=30$; dt $=0\mathrm{.}01$;

$\%$ tf $=$ input$(\text{'}$What is the total time $($s$)?\text{'})$;

$\%$ dt $=$ input$(\text{'}$What is the timestep $($s$)?\text{'})$;

$\%$ Set the initial population values

x$0=22$; xi $=$ x$0$;

y$0=37$; yi $=$ y$0$;

$\%$ Calculate the integer number of steps

nt $=$ ceil$($tf$/$dt$)$;

$\%$ Flag for output within iteration

Out$\_$flag $=$ input$(\text{'}$Display output within iteration?

$(1=$ Yes, $0=$ No$)\text{'})$;

while Out$\_$flag ~$=1$ && Out$\_$flag ~$=0$

fprintf$(\text{'}$ERROR: Incorrect response! Please try again.

$\text{'})$

Out$\_$flag $=$ input$(\text{'}$Display output within iteration?

$(1=$ Yes, $0=$ No$)\text{'})$;

end

$\%$ Start the "for loop"

for i $=1$:$1$:nt

$\%$ Forward Euler Updating Method

xp$1=$ xi $+$ dt$*($a$*$xi $-$ b$*$xi$*$yi$)$;

yp$1=$ yi $+$ dt$*(-$c$*$yi $+$ d$*$xi$*$yi$)$;

$\%$ Update values

xi $=$ xp$1$;

yi $=$ yp$1$;

$\%$ Date Output

if Out$\_$flag $==1$

fprintf$(\text{'}$

The current time is $\%1\mathrm{.}2$f

$\text{'},$i$*$dt$)$

fprintf$(\text{'}$ prey population is $\%1\mathrm{.}2$f

$\text{'},$xi$)$

fprintf$(\text{'}$predator population is $\%1\mathrm{.}2$f

$\text{'},$yi$)$

end

end

$\%$ Display Calculated Solution

fprintf$(\text{'}$

The initial populations are:

$\text{'})$

fprintf$(\text{'}$Prey $=\%1\mathrm{.}4$f

$\text{'},$x$0)$

fprintf$(\text{'}$Predator $=\%1\mathrm{.}4$f

$\text{'},$y$0)$

fprintf$(\text{'}$

After $\%1$d seconds

$\text{'},$tf$)$

fprintf$(\text{'}$with time$-$step $=\%1\mathrm{.}4$f seconds

$\text{'},$dt$)$

fprintf$(\text{'}$

The final populations are:

$\text{'})$

fprintf$(\text{'}$Prey $=\%1\mathrm{.}4$f

$\text{'},$xi$)$

fprintf$(\text{'}$Predator $=\%1\mathrm{.}4$f

$\text{'},$yi$)$

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