Complete the code

Write a MATLAB script to solve our nonhomogeneous drug$-$delivery problem using ode$45.$ Recall that our model is represented as:

$\frac{dD}{dt}=-(k_a+k_d)D+rD0e^{-rt}$

$\frac{dB}{dt}=k_{a}D-k_{m}B$

$\frac{dW}{dt}=k_{d}D+k_{m}B$

Solve for the Timed$-$Release Capsule input function: $f(t)=D_0(1-e^{-rt})$ over the time $0t360$min.

Make sure that the solutions output from ode$45$ is stored to a vector $Y$

Script?

$1\%$ Define constants:

$2ka=0\mathrm{.}025$; $3kd=0\mathrm{.}005$

$3,kd=0\mathrm{.}005$;

$4,km=0\mathrm{.}015$;

$5D0=50$;

$D0=50$; $r=0\mathrm{.}1151$

$-$ absorption rate

$\%($min$^-1-$ digestion rate$)$

$-$ metabolic rate$)$

$\%mg-$ initial dose $\%(mi{n}^{{?}^{?}}-1)-$ Drug release rate

$\%$ Define the anonymous function odefun to represent the system of THREE ODEs to be solved

$\%$ Solve the system of three equations using ode$45$ for all points in time vector, $t$ :

$t=$linspace$(0,6**60,2000)$;

$\%$ Here your ode$45$ output should include the solutions array named $Y($see code below for how $Y$ is used$)$ later

$\%$ Plot solutions:

$D=Y($:$,1)$; $B=Y($:$,2)$;

$B=Y($:$,2)$; $W($:$,3)$;

fig $=$ figure;

fig.Name $=$ 'Numerical Approach'; fig.Color $=\text{'}w\text{'}$;

plot $($t$,$D$,$ t$,$ B$,$ t$,$w$,\text{'}$ linewidth $\text{'},1\mathrm{.}5)$;

xlabel$(\text{'}$time $($min$)\text{'})$; ylabel$(\text{'}$Amount of Drug $($mg$)\text{'})$; title$(\text{'}$Timed Release Capsule'$)$;

$ax=$ gca; ax$.$FontSize $=11$

L $=$ legend$(\text{'}$D$($t$)\text{'},\text{'}$B$($t$)\text{'},\text{'}$W$($t$)\text{'},$ 'orientation $\text{'},$ 'vertical'$)$; L$.$ FontSize $=11$;