In MATLAB, write an ordinary differential equation $($ODE$)$ solver that implements the RK$4$ and RK$5$ methods for approximating an ODE like the methodology performed by the MATLAB function ODE$45.$ This will be produced as a group, but the final solution$/$explanation must be submitted by each student. While the code will be a group effort, the explanation must be done individually. The solver must have the following parts to it:

$*$ The function must receive a differential equation y$=$f$($t$,$y$),$ domain limits $[$t$0,$tn$]$ and initial condition $$f $(0)=$x$$ as inputs.

$*$ The function must adjust the step$-$size on each iteration based on the size of the error between the RK$4$ and RK$5$ methods. $($You are to determine the error$-$size$/$adjustment criterion, implement it and then justify it$.)$

$*$ The function must produce a table which correlates the iteration count, step$-$size, RK$45$ approximation, the true solution, and the error between the two.

$*$Uses the following ODE, initial conditions, and domain: $(,)=()+3$

$(0)=0$

$(0)=1$

$[0,4]$